Stabilization of positive switched systems with time-varying delays under asynchronous switching

This paper investigates the state feedback stabilization problem for a class of positive switched systems with time-varying delays under asynchronous switching in the frameworks of continuous-time and discrete-time dynamics. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and further allowing the functional to increase during the running time of active subsystems, sufficient conditions are provided to guarantee the exponential stability of the resulting closed-loop systems, and the corresponding controller gain matrices and admissible switching signals are presented. Finally, two illustrative examples are given to show the effectiveness of the proposed methods

On feedback stabilization of linear switched systems via switching signal control

Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new algorithms and analyze several mathematical features of the problem which were unnoticed up to now, to our knowledge. We prove complexity results, (in-)equivalence between various notions of stabilizability, existence of Lyapunov functions, and provide a case study for a paradigmatic example introduced by Stanford and Urbano.Comment: 19 pages, 3 figure