Periodic Orbit Analysis of Switched Linear Systems

This paper focuses on the distribution problem of periodic orbits for a class of switched two-dimensional linear systems. A necessary and sufficient condition is proposed to solve the existence problem of periodic solutions for periodically switched linear systems. Then concerning the dwell time irrelated to the initial condition a periodic orbit continuum appears if and only if a periodic orbit exists. In addition, based on the multi-Lyapunov functions, a controller is designed to make the continuum asymptotically stabilize to a periodic orbit. Finally, the theoretical result is explained by a two-DOF manipulator example.