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Robust state feedback $$H_\infty$$ control for uncertain 2-D continuous state delayed systems in the Roesser model. (English) Zbl 1368.93150
Summary: This paper is concerned with the problem of robust state feedback $$H_\infty$$ stabilization for a class of uncertain two-dimensional (2-D) continuous state delayed systems. The parameter uncertainties are assumed to be norm-bounded. Firstly, a new delay-dependent sufficient condition for the robust asymptotical stability of uncertain 2-D continuous systems with state delay is developed. Secondly, a sufficient condition for $$H_\infty$$ disturbance attenuation performance of the given system is derived. Thirdly, a stabilizing state feedback controller is proposed such that the resulting closed-loop system is robustly asymptotically stable and achieves a prescribed $$H_\infty$$ disturbance attenuation level. All results are developed in terms of linear matrix inequalities. Finally, two examples are provided to validate the effectiveness of the proposed method.

##### MSC:
 93B36 $$H^\infty$$-control 93D15 Stabilization of systems by feedback 93D09 Robust stability
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##### References:
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