Reliable L1 control of positive switched systems with time-varying delays

Abstract

This paper deals with the reliable L1 control problem of positive switched systems with time-varying delays. Under the case where both stable and unstable subsystems coexist, sufficient conditions are proposed to guarantee the exponential stability of positive switched systems with time-varying delays, and the average dwell time approach is utilized for the stability analysis. The result is also extended to solve the reliable L1 control problem. All the results are formulated in a set of linear matrix inequalities (LMIs), which can be easily verified or implemented. The obtained theoretical results are demonstrated by a numerical example. © 2013 Xiang and Xiang; licensee Springer.