Stability analysis of two-dimensional switched systems with unstable subsystems

This paper investigates the stability of switched two-dimensional linear systems with unstable subsystems. Based on continuous positive definite functions depending only on the entries of the coefficient matrixes of subsystems, for the case that the origin is a single unstable spiral point of all subsystems, we propose sufficient conditions of stability/instability of the kind of switched systems. Study on an illustrative example and numerical simulations demonstrates the correctness and effectiveness of the new stability/instability results obtained in this paper.