Precise Characterizations of the Stability Margin in Time-Domain Space for Planar Systems Undergoing Periodic Switching

This paper addresses the stability analysis problem for planar periodic switching systems. We characterize the stability margin in the space constituted by the dwell times of the subsystems, by which we can assess the asymptotic stability of the overall system in the necessary and sufficient sense. The mutual constraint conditions on the dwell times in nature depend on the type of equilibrium point of each subsystem. The stability conditions are expressed in terms of a family of transcendental inequalities, which can be numerically solved and precisely depicted in the time-domain space. An example is worked out in detail to illustrate the theoretical results.