Safety-Critical Stabilizing Design of Switched Linear Autonomous Systems

For continuous-time switched linear autonomous systems, this work addresses the stabilization problem under safety-critical constraints. Given an origin-symmetric region that any state trajectory should be stayed, we seek to design a switching law to achieve both stability and safety. The main approach is to characterize, both theoretically and algorithmically, the safe initial set that any initial state within the set could stay in the given safety region with a properly designed switching law. Technically, we develop a design procedure that could approximate the safe initial set with the help of the pathwise state feedback switching strategy. A third-order example is presented to validate the effectiveness of the proposed methodology.