Stability and stabilization for switched systems with all subsystems unstable

This paper investigates the stability and stabilization for switched systems with all modes unstable. Firstly, a class of periodic switching signal is proposed to ensure that the considered system is global asymptotical stability (GAS) on continuous-time interval. The quadratic Lyapunov function is permitted to increase on the part of a complete switching period. Secondly, the state feedback controllers are designed to stabilize each subsystem, and the sufficient condition of stabilization is provided for the non-autonomous switched system. Two numerical examples are finally presented to verify the validity of the obtained theoretical results.