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SUMMARYThis paper is concerned with the problem of H 1 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 closedloop 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 1 performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuoustime 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.

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This article is concerned with the existence problem of a common linear copositive Lyapunov function (CLCLF) for switched positive linear systems with stable and pairwise commutable subsystems. Three families of such systems composed of only continuous-time subsystems, only discrete-time subsystems and mixed continuous-and discrete-time subsystems are considered, respectively. It is demonstrated that a CLCLF can always be constructed for the underlying system whenever its subsystems are continuous-time, discrete-time or the mixed type. The case when the number of subsystems is two is first considered, then the obtained result is extended to the general case. Three numerical examples are given to verify the validity of the developed results.