Finite-time boundedness and l1-gain analysis for discrete positive switched systems with time-varying delay

This paper is concerned with the problem of finite-time l₁-gain boundedness for a class of positive switched discrete-time linear systems with time-varying delay. This kind of systems have the property that the states take nonnegative values whenever the initial boundaries are non-negative. Firstly, by using the average dwell time approach, sufficient conditions which can ensure the underlying system to be finite-time bounded are given. Then, the performance of finite-time l₁-gain is studied. These conditions are given in terms of linear matrix inequalities (LMIs) which can be solved conveniently. Finally, an example is given to illustrate the efficiency of the proposed method.