Finite‐time stability and finite‐time weighted <i>L</i> ₂ ‐gain analysis for switched systems with time‐varying delay

Abstract

Finite‐time stability and finite‐time boundedness for a class of switched linear systems with time‐varying delay are studied. Sufficient conditions which guarantee switched linear systems with time‐varying delay finite‐time stable or finite‐time bounded are presented. These conditions are delay‐dependent and are given in terms of linear matrix inequalities. Average dwell time of switching signals is also given such that switched linear systems are finite‐time stable or finite‐time bounded. Moreover, finite‐time weighted L 2 ‐gain of switched linear systems with time‐varying delay are also given to measure its disturbance tolerance capability in the fixed time interval. Detail proofs are accomplished by using multiple Lyapunov‐like functions. An example is employed to verify the efficiency of the proposed method.