Robust stability of switched positive linear systems with interval uncertainties via multiple time-varying linear copositive Lyapunov functions

This paper studies the robust stability analysis of a class of switched positive linear systems with uncertainties in the framework of dwell time switching. The uncertainties refer to interval uncertainties. Two classes of dwell time switching signals are considered in this paper: (i) the first class is confined by a certain pair of upper and lower bounds; (ii) the other is the minimum dwell time. First, a class of multiple time-varying linear copositive Lyapunov functions is constructed to analyze the robust stability of the studied switched system. Then, under the pre-given dwell time switching, the sufficient conditions are obtained by restricting the decay of the Lyapunov functions of the active subsystem and forcing “energy” of the overall switched system to decrease at switching instants by the proposed Lyapunov functions. All present conditions are solvable in terms of linear programming. An example is considered in order to emphasize the effectiveness of the proposed approach.