Stabilization and controller design of positive switched linear systems with all subsystems unstable

In this letter, a mixed min-switching strategy for the stabilization of positive switched linear systems with unstable subsystems is proposed. With the aid of piecewise continuous switched linear time-varying Lyapunov function method, we give some novel criteria such that the system remains asymptotically stable and apply these results to the stability problem of a simple switched genetic regulatory network. The time-varying state feedback controller is developed to guarantee the system is asymptotically stable under the mixed min-switching signal. Furthermore, numerical examples illustrate that the theoretical results presented in this paper are better than existing ones.