Exponential stability for positive systems with bounded time-varying delays and static output feedback stabilization

This paper investigates the problem of exponential stability analysis and static output feedback stabilization for discrete-time and continuous-time positive systems with bounded time-varying delays. Based on the relationship between the solution to the system with time-varying delay and that to the corresponding system with constant delay under specific conditions, the equivalence between the α-exponential stability of such two types of systems is established. Then some necessary conditions and sufficient conditions are provided for α-exponential stability of positive systems with bounded time-varying delays. It is shown that, for such systems, the exponential stability with given decay rate is closely related to the bound of the delay. Then by using the singular value decomposition approach, sufficient conditions for the existence of static output feedback controllers are established in terms of linear programming (LP) problems. Some illustrative examples are given to show the correctness of the obtained theoretical results.