Characterization and Computation of Invariant Sets for Constrained Switched Systems

Abstract

Standard results in the study of switched systems mostly consider unconstrained models with arbitrary switching functions. This thesis focuses on the stability of constrained switched systems when the switching function satisfies some minimal dwell-time requirement. Main contributions of the thesis include (i) a necessary and sufficient condition for the stability of switched systems when the switching function satisfies dwell-time requirement; (ii) an algorithm that computes the minimal common dwell-time needed for stability; (iii) a constructive procedure for computing the minimal mode-dependent dwell-times (mode-dependent dwell-times refers to the case where one dwell-time is used for each mode); (iv) a new characterization of robust invariant sets for dwell-time switched systems subject to disturbance inputs and constraints; and (v) algorithms that compute the minimal and maximal convex robust invariant sets under dwell-time considerations.

The above contributions are for the case where either a common dwell-time or mode-dependent dwell-times are imposed on the switched systems. They can be seen as the generalization of the special case where the system switches arbitrarily among the various modes. Finally, some of the above-mentioned theoretical results are applied to the problem of controlling the read/write head of a Hard Disk Drive (HDD) system. A mode switching control scheme with controller initialization is proposed that improves the performance of the HDD system compared to the conventional switching schemes.