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Relevant bibliographies by topics / Parametric polynomial systems

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Academic literature on the topic 'Parametric polynomial systems'

Author: Grafiati

Published: 25 May 2024

Last updated: 19 July 2025

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Journal articles on the topic "Parametric polynomial systems"

1

Franco-Medrano, Fermin, and Francisco J. Solis. "Stability of Real Parametric Polynomial Discrete Dynamical Systems." Discrete Dynamics in Nature and Society 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/680970.

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We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameterλand generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to realmth degree real polynomial maps. In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points. In order to do this, we have introduced the concept ofcanonical polynomial mapswhich are topologically conjugate to any polynomial map of the same degree with real fixed points. The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termedProduct Position Functionfor a given fixed point. The values of this product position determine the stability of the fixed point in question, when it bifurcates and even when chaos arises, as it passes through what we have termedstability bands. The exact boundary values of these stability bands are yet to be calculated for regions of type greater than one for polynomials of degree higher than three.

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Lazard, Daniel, and Fabrice Rouillier. "Solving parametric polynomial systems." Journal of Symbolic Computation 42, no. 6 (2007): 636–67. http://dx.doi.org/10.1016/j.jsc.2007.01.007.

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Lai, Yisheng, Renhong Wang, and Jinming Wu. "Solving parametric piecewise polynomial systems." Journal of Computational and Applied Mathematics 236, no. 5 (2011): 924–36. http://dx.doi.org/10.1016/j.cam.2011.05.008.

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Moreno Maza, Marc, Bican Xia, and Rong Xiao. "On Solving Parametric Polynomial Systems." Mathematics in Computer Science 6, no. 4 (2012): 457–73. http://dx.doi.org/10.1007/s11786-012-0136-3.

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Ayad, A. "Complexity of solving parametric polynomial systems." Journal of Mathematical Sciences 179, no. 6 (2011): 635–61. http://dx.doi.org/10.1007/s10958-011-0616-z.

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Hashemi, Amir, Benyamin M.-Alizadeh, and Mahdi Dehghani Darmian. "Minimal polynomial systems for parametric matrices." Linear and Multilinear Algebra 61, no. 2 (2012): 265–72. http://dx.doi.org/10.1080/03081087.2012.670235.

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Chen, Zhenghong, Xiaoxian Tang, and Bican Xia. "Generic regular decompositions for parametric polynomial systems." Journal of Systems Science and Complexity 28, no. 5 (2015): 1194–211. http://dx.doi.org/10.1007/s11424-015-3015-6.

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Gerhard, Jürgen, D. J. Jeffrey, and Guillaume Moroz. "A package for solving parametric polynomial systems." ACM Communications in Computer Algebra 43, no. 3/4 (2010): 61–72. http://dx.doi.org/10.1145/1823931.1823933.

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A.A., Nesenchuk. "Investigation and robust synthesis of polynomials under perturbations based on the root locus parameter distribution diagram." Artificial Intelligence 24, no. 1-2 (2019): 25–33. http://dx.doi.org/10.15407/jai2019.01-02.025.

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Investigation of the 4 th order dynamic systems characteristic polynomials behavior in conditions of the interval parametric uncertainties is carried out on the basis of root locus portraits. The roots behavior regularities and corresponding diagrams for the root locus parameter distribution along the asymptotic stability bound are specified for the root locus portraits of the systems. On this basis the stability conditions are derived, graphic-analytical method is worked out for calculating intervals of variation for the polynomial family parameters ensuring its robust stability. The discovered regularities of the system root locus portrait behavior allow to extract hurwitz sub-families from the non-hurwitz families of interval polynomials and to determine whether there exists at least one stable polynomial in the unstable polynomial family.

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HOANG, VIET HA, and CHRISTOPH SCHWAB. "REGULARITY AND GENERALIZED POLYNOMIAL CHAOS APPROXIMATION OF PARAMETRIC AND RANDOM SECOND-ORDER HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS." Analysis and Applications 10, no. 03 (2012): 295–326. http://dx.doi.org/10.1142/s0219530512500145.

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Initial boundary value problems of linear second-order hyperbolic partial differential equations whose coefficients depend on countably many random parameters are reduced to a parametric family of deterministic initial boundary value problems on an infinite dimensional parameter space. This parametric family is approximated by Galerkin projection onto finitely supported polynomial systems in the parameter space. We establish uniform stability with respect to the support of the resulting coupled hyperbolic systems, and provide sufficient smoothness and compatibility conditions on the data for the solution to exhibit analytic, respectively, Gevrey regularity with respect to the countably many parameters. Sufficient conditions for the p-summability of the generalized polynomial chaos expansion of the parametric solution in terms of the countably many input parameters are obtained and rates of convergence of best N-term polynomial chaos type approximations of the parametric solution are given. In addition, regularity both in space and time for the parametric family of solutions is proved for data satisfying certain compatibility conditions. The results allow obtaining convergence rates and stability of sparse space-time tensor product Galerkin discretizations in the parameter space.

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Dissertations / Theses on the topic "Parametric polynomial systems"

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Fotiou, Ioannis A. "Parametric optimization and constrained optimal control for polynomial dynamical systems." Zürich : ETH, 2008. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=17609.

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Le, Huu Phuoc. "On solving parametric polynomial systems and quantifier elimination over the reals : algorithms, complexity and implementations." Electronic Thesis or Diss., Sorbonne université, 2021. http://www.theses.fr/2021SORUS554.

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La résolution de systèmes polynomiaux est un domaine de recherche actif situé entre informatique et mathématiques. Il trouve de nombreuses applications dans divers domaines des sciences de l'ingénieur (robotique, biologie) et du numérique (cryptographie, imagerie, contrôle optimal). Le calcul formel fournit des algorithmes qui permettent de calculer des solutions exactes à ces applications, ce qui pourraient être très délicat pour des algorithmes numériques en raison de la non-linéarité. La plupart des applications en ingénierie s'intéressent aux solutions réelles. Le développement d'algorithmes permettant de les traiter s'appuie sur les concepts de la géométrie réelle effective ; la classe des ensembles semi-algébriques en constituant les objets de base. Cette thèse se concentre sur trois problèmes ci-dessous, qui apparaissent dans de nombreuses applications et sont largement étudié en calcul formel : - Classifier les solutions réelles d'un système polynomial paramétrique par les valeurs des paramètres; - Élimination de quantificateurs; - Calcul des points isolés d'un ensemble semi-algébrique. Nous concevons de nouveaux algorithmes symboliques avec une meilleure complexité que l'état de l'art. En pratique, nos implémentations efficaces de ces algorithmes sont capables de résoudre des problèmes hors d'atteinte des logiciels de l'état de l'art<br>Solving polynomial systems is an active research area located between computer sciences and mathematics. It finds many applications in various fields of engineering and sciences (robotics, biology, cryptography, imaging, optimal control). In symbolic computation, one studies and designs efficient algorithms that compute exact solutions to those applications, which could be very delicate for numerical methods because of the non-linearity of the given systems. Most applications in engineering are interested in the real solutions to the system. The development of algorithms to deal with polynomial systems over the reals is based on the concepts of effective real algebraic geometry in which the class of semi-algebraic sets constitute the main objects. This thesis focuses on three problems below, which appear in many applications and are widely studied in computer algebra and effective real algebraic geometry: - Classify the real solutions of a parametric polynomial system according to the parameters' value; - Elimination of quantifiers; - Computation of the isolated points of a semi-algebraic set. We designed new symbolic algorithms with better complexity than the state-of-the-art. In practice, our efficient implementations of these algorithms are capable of solving applications beyond the reach of the state-of-the-art software

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Hays, Joseph T. "Parametric Optimal Design Of Uncertain Dynamical Systems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/28850.

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This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost.<br>Ph. D.

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Blanchard, Emmanuel. "Polynomial Chaos Approaches to Parameter Estimation and Control Design for Mechanical Systems with Uncertain Parameters." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/26727.

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Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo approaches for quantifying the effects of such uncertainties on the system response. This work uses the polynomial chaos framework to develop new methodologies for the simulation, parameter estimation, and control of mechanical systems with uncertainty. This study has led to new computational approaches for parameter estimation in nonlinear mechanical systems. The first approach is a polynomial-chaos based Bayesian approach in which maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. The second approach is based on the Extended Kalman Filter (EKF). The error covariances needed for the EKF approach are computed from polynomial chaos expansions, and the EKF is used to update the polynomial chaos representation of the uncertain states and the uncertain parameters. The advantages and drawbacks of each method have been investigated. This study has demonstrated the effectiveness of the polynomial chaos approach for control systems analysis. For control system design the study has focused on the LQR problem when dealing with parametric uncertainties. The LQR problem was written as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework. The solution to the Hâ problem as well as the H2 problem can be seen as extensions of the LQR problem. This method might therefore have the potential of being a first step towards the development of computationally efficient numerical methods for Hâ design with parametric uncertainties. I would like to gratefully acknowledge the support provided for this work under NASA Grant NNL05AA18A.<br>Ph. D.

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Feijoo, Juan Alejandro Vazquez. "Analysis and identification of nonlinear system using parametric models of Volterra operators." Thesis, University of Sheffield, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274962.

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Schost, Eric. "Sur la resolution des systemes polynomiaux a parametres." Palaiseau, Ecole polytechnique, 2000. http://www.theses.fr/2000EPXX0056.

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Le sujet de cette these est la resolution des systemes polynomiaux dependant de parametres ; on considere en priorite des systemes ayant autant d'inconnues que d'equations. L'objectif est d'obtenir une description des inconnues en fonction des parametres, valable generiquement. On s'interesse tout d'abord a une representation utilisant un element primitif, avant de se tourner vers une representation triangulaire. Nous proposons des estimations a priori sur la taille (degre ou hauteur) de ces objets, puis des algorithmes probabilistes pour les calculer, bases sur une representation de l'entree par un calcul d'evaluation. Ces algorithmes sont implantes en magma. Le texte en presente des applications, dans le domaine du calcul effectif sur les courbes hyperelliptiques, de la geometrie reelle et du calcul d'invariants. Par ailleurs, nous presentons une extension de ces idees au cas d'une situation surdeterminee dependant de parametres.

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Books on the topic "Parametric polynomial systems"

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Center, Langley Research, ed. On the numerical formulation of parametric linear fractional transformation (LFT) uncertainty models for multivariate matrix polynomial problems. National Aeronautics and Space Administration, Langley Research Center, 1998.

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Contemporary Precalculus through Applications. North Carolina School of Science and Mathematics, 2021. http://dx.doi.org/10.5149/9781469665924_departmentofmathematics.

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The first edition of Contemporary Precalculus through Applications was published in 1993, well before the widespread use of computers in the classroom. Collaborating with students and teachers across the state, faculty from the North Carolina School of Science and Mathematics (NCSSM) have steadily developed, reviewed, and tested the textbook in the years since. It is the sole textbook used in NCSSM precalculus courses. This third edition contains extensively updated data, graphics, and material attuned to contemporary technology while keeping what made the book so revolutionary when it was first published—a focus on real-world problem solving and student discovery. This edition will prepare students to learn mathematics in the following major areas: · Data analysis and linear regression · Functions: linear, polynomial, rational, exponential, logarithmic, parametric, and trigonometric · Modifying functions through transformations and compositions · Recursive systems and sequences · Modeling real-world phenomenon and applications An open access edition of this book is available at cpta.ncssm.edu, along with supplementary materials and other information.

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Algebraic Statistics. American Mathematical Society, 2018.

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Book chapters on the topic "Parametric polynomial systems"

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Chen, Changbo, and Marc Moreno Maza. "Solving Parametric Polynomial Systems by RealComprehensiveTriangularize." In Mathematical Software – ICMS 2014. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44199-2_76.

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Hong, Hoon, and Thomas Sturm. "Positive Solutions of Systems of Signed Parametric Polynomial Inequalities." In Developments in Language Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99639-4_17.

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Montes, Antonio, and Michael Wibmer. "Software for Discussing Parametric Polynomial Systems: The Gröbner Cover." In Mathematical Software – ICMS 2014. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44199-2_62.

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Eaves, B. Curtis, and Uriel G. Rothblum. "Arithmetic Continuation of Regular Roots of Formal Parametric Polynomial Systems." In Computational Optimization. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5197-3_10.

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Lewis, Robert H. "Dixon-EDF: The Premier Method for Solution of Parametric Polynomial Systems." In Applications of Computer Algebra. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56932-1_16.

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Zhou, Jie, and Dingkang Wang. "A Method to Determine if Two Parametric Polynomial Systems Are Equal." In Mathematical Software – ICMS 2014. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44199-2_81.

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Chesi, Graziano, Andrea Garulli, Alberto Tesi, and Antonio Vicino. "An LMI-Based Technique for Robust Stability Analysis of Linear Systems with Polynomial Parametric Uncertainties." In Positive Polynomials in Control. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/10997703_5.

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Chen, Changbo, and Wenyuan Wu. "Revealing Bistability in Neurological Disorder Models By Solving Parametric Polynomial Systems Geometrically." In Artificial Intelligence and Symbolic Computation. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99957-9_11.

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Pillonetto, Gianluigi, Tianshi Chen, Alessandro Chiuso, Giuseppe De Nicolao, and Lennart Ljung. "Regularization for Nonlinear System Identification." In Regularized System Identification. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95860-2_8.

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AbstractIn this chapter we review some basic ideas for nonlinear system identification. This is a complex area with a vast and rich literature. One reason for the richness is that very many parameterizations of the unknown system have been suggested, each with various proposed estimation methods. We will first describe with some details nonparametric techniques based on Reproducing Kernel Hilbert Space theory and Gaussian regression. The focus will be on the use of regularized least squares, first equipped with the Gaussian or polynomial kernel. Then, we will describe a new kernel able to account for some features of nonlinear dynamic systems, including fading memory concepts. Regularized Volterra models will be also discussed. We will then provide a brief overview on neural and deep networks, hybrid systems identification, block-oriented models like Wiener and Hammerstein, parametric and nonparametric variable selection methods.

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Chen, Changbo, and Wenyuan Wu. "A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications." In Computer Algebra in Scientific Computing. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45641-6_11.

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Conference papers on the topic "Parametric polynomial systems"

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Dong, Rina, Dong Lu, Chenqi Mou, and Dongming Wang. "Comprehensive Characteristic Decomposition of Parametric Polynomial Systems." In ISSAC '21: International Symposium on Symbolic and Algebraic Computation. ACM, 2021. http://dx.doi.org/10.1145/3452143.3465536.

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Afef, Marai Ghanmi, Hajji Sofien, and Kamoun Samira. "Parametric and state estimation for nonlinear polynomial systems." In 2017 18th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA). IEEE, 2017. http://dx.doi.org/10.1109/sta.2017.8314953.

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Arikawa, Keisuke. "Kinematic Analysis of Mechanisms Based on Parametric Polynomial System." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85347.

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Many kinematic problems of mechanisms can be expressed in the form of polynomial systems. Gröbner Bases computation is effective for algebraically analyzing such systems. In this research, we discuss the cases in which the parameters are included in the polynomial systems. The parameters are used to express the link lengths, the displacements of active joints, hand positions, and so on. By calculating Gröbner Cover of the parametric polynomial system that expresses kinematic constraints, we obtain segmentation of the parameter space and valid Gröbner Bases for each segment. In the application examples, we use planar linkages to interpret the meanings of the algebraic equations that define the segments and the Gröbner Bases. Using these interpretations, we confirmed that it was possible to enumerate the assembly and working modes and to identify the geometrical conditions that enable overconstrained motions.

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Vataeva, E. Yu, V. F. Shishlakov, D. V. Shishlakov, and N. V. Reshetnikova. "Parametric Synthesis of Nonlinear Automatic Control Systems with Polynomial Approximation." In 2019 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF). IEEE, 2019. http://dx.doi.org/10.1109/weconf.2019.8840123.

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Wang, Yan, and David M. Bevly. "Robust Observer Design for Lipschitz Nonlinear Systems With Parametric Uncertainty." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-4104.

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This paper discusses optimal and robust observer design for the Lipschitz nonlinear systems. The stability analysis for the Lure problem is first reviewed. Then, a two-DOF nonlinear observer is proposed so that the observer error dynamic model can be transformed to an equivalent Lure system. In this framework, the difference of the nonlinear parts in the vector fields of the original system and observer is modeled as a nonlinear memoryless block that is covered by a multivariable sector condition or an equivalent semi-algebraic set defined by a quadratic polynomial inequality. Then, a sufficient condition for asymptotic stability of the observer error dynamics is formulated in terms of the feasibility of polynomial matrix inequalities (PMIs), which can be solved by Lasserre’s moment relaxation. Furthermore, various quadratic performance criteria, such as H2 and H∞, can be easily incorporated in this framework. Finally, a parameter adaptation algorithm is introduced to cope with the parameter uncertainty.

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Sindia, Suraj, Virendra Singh, and Vishwani D. Agrawal. "Parametric Fault Diagnosis of Nonlinear Analog Circuits Using Polynomial Coefficients." In 2010 23rd International Conference on VLSI Design: concurrently with the 9th International Conference on Embedded Systems Design (VLSID). IEEE, 2010. http://dx.doi.org/10.1109/vlsi.design.2010.81.

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Yong Hoon Jang, Jin Bae Park, and Young Hoon Joo. "A robust stabilization of discrete-time polynomial fuzzy systems with parametric uncertainties." In 2016 International Conference on Fuzzy Theory and Its Applications (iFuzzy). IEEE, 2016. http://dx.doi.org/10.1109/ifuzzy.2016.8004938.

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Moroz, Guillaume. "Complexity of the resolution of parametric systems of polynomial equations and inequations." In the 2006 international symposium. ACM Press, 2006. http://dx.doi.org/10.1145/1145768.1145810.

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Prasad, Aditi K., and Sourajeet Roy. "Mixed epistemic-aleatory uncertainty quantification using reduced dimensional polynomial chaos and parametric ANOVA." In 2017 IEEE 26th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS). IEEE, 2017. http://dx.doi.org/10.1109/epeps.2017.8329716.

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Hays, Joe, Adrian Sandu, Corina Sandu, and Dennis Hong. "Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62789.

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This work presents a novel optimal design framework that treats uncertain dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness and suboptimal performance. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The uncertainty statistics are explicitly included in the optimization process. Systems that are nonlinear, have active constraints, or opposing design objectives are shown to benefit from the new framework. Specifically, using a constraint-based multi-objective formulation, the direct treatment of uncertainties during the optimization process is shown to shift, or off-set, the resulting Pareto optimal trade-off curve. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design that accounts for the entire family of systems within the associated probability space.

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