Stabilizing Design for a Class of Continuous-Time Switched Linear Control Systems

In this work, we investigate the feedback stabilization problem for a class of single-input continuous-time switched linear systems. When the system is completely controllable, we propose a method to construct multi-linear feedback controllers for one subsystem to achieve system stability. When the switched system is incompletely controllable, we prove that the switched linear system is multi-linear state feedback consistently asymptotically stabilizable if and only if the uncontrollable sub-mode is consistently asymptotically stabilizable, and design a time-driven switching path to stabilize both the controllable sub-mode and uncontrollable sub-mode. Finally, a numerical example is presented to exhibit the effectiveness of the proposed design methodology.