Feedback Stabilization of Third-Order Switched Linear Control Systems

In this letter, we address the stabilization problem for third-order continuous-time switched linear control systems. We prove that the switched system is stabilizable iff the uncontrollable sub-mode is stabilizable. For completely controllable switched systems, multi-linear feedback controllers are assigned to one subsystem in a time-varying manner. For incompletely controllable switched systems, mixed time-driven and state-driven switching laws are designed to stabilize both the controllable sub-mode and uncontrollable sub-mode. Two numerical examples are presented to exhibit the effectiveness of the proposed design methodology.