Positive $$L_1 $$ L 1 Observer Design for Positive Switched Systems

Abstract

This paper investigates the problem of $$L_1$$ L 1 observer design for positive switched systems. Firstly, a new kind of positive $$L_1$$ L 1 observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive $$L_1$$ L 1 observer. Under the condition obtained, the estimated error converges to zero exponentially, and the $$L_1$$ L 1 -gain from the disturbance input to the estimated error is less than a prescribed level. Then the proposed design result is extended to positive switched systems with mixed time-varying delays, where the mixed time-varying delays are presented in the form of discrete delay and distributed delay. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.