Positive l<inf>1</inf> observer design for positive switched systems with time-varying delays via delta operator approach

This paper investigates the problem of l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> observer design for positive switched systems with time-varying delays via delta operator approach. The purpose is to design a positive observer such that the estimated error exponentially converges to zero and the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -gain from the disturbance input to the estimated error is less than a prescribed level. Based on the average dwell time approach, a sufficient condition for the existence of a positive l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> observer for the considered system is established by constructing an appropriate co-positive type Lyapunov-Krasovskii functional in delta domain. Finally, a numerical example is presented to explicitly demonstrate the effectiveness and feasibility of the proposed method.