Robust reliable control of uncertain 2D discrete switched systems with state delays

TL;DR

This paper develops a robust control method for uncertain 2D discrete switched systems with delays, ensuring stability despite uncertainties and actuator failures using LMIs and dwell time techniques.

Contribution

It introduces a delay-dependent stability condition and extends the average dwell time concept to 2D switched systems for robust control design.

Findings

Delay-dependent stability condition established

Reliable state feedback controller designed via LMIs

Effective control demonstrated through example

Abstract

This paper is concerned with the problem of robust reliable control for a class of uncertain 2D discrete switched systems with state delays represented by a model of Roesser type. The parameter uncertainties are assumed to be norm-bounded. Firstly, delay-dependent sufficient condition for the exponential stability of the discrete 2D systems with state delays is established. Then, the concept of average dwell time is extended to 2D switched systems, and a reliable state feedback controller is developed in terms of linear matrix inequalities (LMIs) such that the resulting closed-loop system is exponentially stable for all admissible uncertainties and actuator failures. The dwell time approach is utilized for the stability analysis and controller design. Finally, an example is included to demonstrate the effectiveness of the proposed approach.