Error reachable set based stabilization of switched linear systems with bounded peak disturbances

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time (PDT) constraint. A double-clock-dependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system, and assign to each system a controller scheduled by a clock. A necessary and sufficient convex stability criterion is presented for the nominal system, and is further extended to the stabilization controller design with a nominal clock. In the presence of bounded peak disturbances, another stabilization controller with an error clock is developed for the error system, with the purpose of “minimizing” the reachable set of the error system by the ellipsoidal techniques. It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system, i.e., a union of a family of bounding ellipsoids, that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system. Two numerical examples are provided to verify the effectiveness of the developed results.