Weighted H_∞ control with D -stability constraint for switched positive linear systems

This paper is concerned with the problem of H∞ control with D-stability constraint for a class of switched positive linear systems. The D-stability means that all the poles of each subsystem of the resultant closed-loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state-feedback controllers, which guarantees that the closed-loop system is not only positive and exponentially stable with each subsystem D-stable but also has a weighted H∞ performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous-time and discrete-time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.