De Souza, Carlos E.; Osowsky, Jefferson Gain-scheduled control of two-dimensional discrete-time linear parameter-varying systems in the Roesser model. (English) Zbl 1257.93058 Automatica 49, No. 1, 101-110 (2013). 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. Cited in 5 Documents MSC: 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory 93B36 \(H^\infty\)-control Keywords:two-dimensional systems; gain-scheduled control; \(H_{\infty }\) control; guaranteed cost control; linear parameter-varying systems; discrete-time systems; parameter-dependent Lyapunov function PDFBibTeX XMLCite \textit{C. E. De Souza} and \textit{J. Osowsky}, Automatica 49, No. 1, 101--110 (2013; Zbl 1257.93058) Full Text: DOI