Robust state feedback for uncertain 2-D discrete switched systems in the Roesser model

Abstract

The design of robust $H_{\mathrm{\infty }}$ controllers is considered here for a class of two-dimensional (2-D) discrete switched systems described by the Roesser model with polytopic uncertainties. Attention focuses on the design of a switched state feedback controller, which guarantees the robust asymptotic stability and a prescribed $H_{\mathrm{\infty }}$ performance for the closed-loop system. By using multiple parameter-dependent Lyapunov functionals, and introducing some switched free-weighting matrices, a new sufficient condition for the robust $H_{\mathrm{\infty }}$ performance analysis of uncertain 2-D discrete switched systems is developed. Furthermore, the design of switched state feedback controller is proposed in terms of linear matrix inequalities (LMIs). Illustrative examples are given to illustrate the effectiveness of the developed theoretical results.

Keywords:

• 2-D discrete switched systems
• polytopic uncertainties
• robust $H_{\mathrm{\infty }}$ control
• linear matrix inequalities (LMIs)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Fernando Tadeo is funded by the Regional Government of Castilla y Leon and EU-FEDER funds [CLU 2017-09 and UIC 233]. The other authors are funded by Centre National pour la Recherche Scientifique et Technique of Morocco [9USMBA2017].