Yet Another Computation-Oriented Necessary and Sufficient Condition for Stabilizability of Switched Linear Systems

• Published in: IEEE transactions on automatic control Vol. 67; no. 7; pp. 3627 - 3632
• Main Author: Fiacchini, Mirko
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-07-2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Automatic; Convergence; Convex analysis; Discrete time systems; Dynamical Systems; Engineering Sciences; Heuristic algorithms; Linear systems; Mathematics; Partitioning algorithms; Stability analysis; stabilizability; switched linear systems; Switched systems; Switches; convex analysis; Switched linear systems; stabilizability
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3103872

This article presents a computational method to test the stabilizability of discrete-time switched linear systems. The existence of a conic cover of the space on whose elements a convex condition holds is proved to be necessary and sufficient for stabilizability. An algorithm for computing a conic partition that satisfies the new necessary and sufficient condition is given. The algorithm, which allows us to determine bounds on the exponential convergence rate, is proved to overcome the conservatism of conditions equivalent to periodic stabilizability and is applied to a 4-D system.