Exponential stabilization of second-order switched systems: Necessary and sufficient conditions

The stabilizability problem of planar switched systems is investigated. Based on the polar-coordinates interpretation, the intrinsical connections between the conic switching rule and the qualitative features of the subsystems are presented. Therefore, necessary and sufficient stabilizability conditions are established. The stabilizing switching rules are categorized into two types, termed swinging switching and whirling switching, which both constitute the periodic switching sequences. Moreover, the convergence of the forced trajectory is exhibited in a uniform manner. Illustrative examples are provided to demonstrate our result.