Finite-time L1 control for positive switched linear systems with time-varying delay

• Sufficient conditions for the existence of finite-time boundedness for positive switched delay systems are proposed.
• L1 performance for positive switched delay systems is investigated via the average dwell time approach.
• A state feedback controller is designed to stabilize positive switched delay systems.

This paper is concerned with the problem of finite-time L1 control for a class of positive switched linear systems with time-varying delay. Firstly, by using the average dwell time approach, sufficient conditions which can guarantee the L1 finite-time boundedness of the underlying system are given. Then, in virtue of the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with L1-gain performance. All the obtained results are formulated 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.