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Robust \(\mathcal H_{\infty}\) fuzzy filter design for uncertain nonlinear singularly perturbed systems with Markovian jumps: an LMI approach. (English) Zbl 1113.93078

Summary: This paper examines the problem of designing a robust \(\mathcal H_{\infty}\) fuzzy filter for a singularly perturbed Takagi - Sugeno (TS) fuzzy system with Markovian jumps. Based on a linear matrix inequality (LMI) approach, sufficient conditions for the existence of a robust \(\mathcal H_{\infty}\) fuzzy filter are derived in terms of a family of LMIs. To alleviate the numerical stiffness resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation \(\varepsilon\). The proposed approach does not involve the separation of states into slow and fast ones and it can be applied to both standard and nonstandard nonlinear singularly perturbed systems. A numerical example is provided to illustrate the design developed in this paper.

MSC:

93C70 Time-scale analysis and singular perturbations in control/observation systems
93C41 Control/observation systems with incomplete information
93C42 Fuzzy control/observation systems
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory

Software:

LMI toolbox
PDFBibTeX XMLCite
Full Text: DOI

References:

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