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Gain-scheduled control of two-dimensional discrete-time linear parameter-varying systems in the Roesser model. (English) Zbl 1257.93058

Summary: This paper is concerned with gain-scheduled control of two-dimensional discrete-time linear parameter-varying systems described by a Roesser state-space model with matrices depending affinely on time-varying scheduling parameters. The parameter admissible values and variations are assumed to belong to given intervals. Linear matrix inequality based methods are devised for designing static state feedback gain-scheduled controllers with either an \(H_{\infty }\) or quadratic regulator-type performance. The control designs build on quadratically parameter-dependent Lyapunov functions and allow for incorporating information on available bounds on the parameters variation. The proposed controller gain can be independent, affine, quadratic, or a matrix fraction of quadratic polynomial matrices in the scheduling parameters.

MSC:

93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
93B36 \(H^\infty\)-control
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