Robust state feedback \(H_\infty \) control for uncertain 2-D continuous state delayed systems in the Roesser model.

*(English)*Zbl 1368.93150Summary: 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.

##### Keywords:

2-D continuous systems; time-varying delays; state feedback; \(H_\infty \) performance; Roesser model; robust stability
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\textit{I. Ghous} and \textit{Z. Xiang}, Multidimensional Syst. Signal Process. 27, No. 2, 297--319 (2016; Zbl 1368.93150)

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