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Stabilization and local stability analysis of continuous-time nonlinear systems represented by Takagi-Sugeno fuzzy models

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Gomes, Izabella Thaís Oliveira
Total Authors: 1
Document type: Master's Dissertation
Institution: Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
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This dissertation addresses the problems of local stability analysis, estimation of domains of attraction, and local state-feedback stabilization for continuous time nonlinear systems represented by Takagi-Sugeno (T¿S) fuzzy models. Sufficient conditions, expressed in terms of parameter-dependent Linear Matrix Inequalities (LMIs), are given to certify the local stability and for control design, based on homogenous polynomial Lyapunov matrices and slack variables of arbitrary degree. By using a polytopic representation for the time-derivative of the membership functions of the T-S model, upper bounds for the variation rates are not required. As an additional contribution, nonlinear terms of the Jacobian matrix associated with the T¿S model are replaced, whenever possible, by the corresponding Taylor series, truncated at a predetermined order, avoiding the definition of a new set of uncertain parameters, which would increase the complexity of the representation. Examples borrowed from the T¿S literature are used to illustrate that the proposed methods provide better results than other approaches in terms of larger estimates for the regions of attraction, both in the case of stability analysis and in the synthesis of state-feedback stabilizing controllers. A study about the use of linear programming, as an alternative to specialized LMI solvers, for stability analysis of uncertain linear systems is also included in the dissertation (AU)

FAPESP's process: 17/18785-5 - Parameter-Dependent Linear Matrix Inequalities Applied to Stability Analysis and Synthesis of Controllers and Filters for Uncertain Dynamic Systems
Grantee:Pedro Luis Dias Peres
Support type: Regular Research Grants