Generating Functions of Switched Linear Systems: Analysis, Computation, and Stability Applications
Links to Files
Author/Creator
Author/Creator ORCID
Date
Type of Work
Department
Program
Citation of Original Publication
Hu, Jianghai, Jinglai Shen, and Wei Zhang. “Generating Functions of Switched Linear Systems: Analysis, Computation, and Stability Applications.” IEEE Transactions on Automatic Control 56, no. 5 (May 2011): 1059–74. https://doi.org/10.1109/TAC.2010.2067590.
Rights
© 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Abstract
In this paper, a unified framework is proposed to study the exponential stability of discrete-time switched linear systems and, more generally, the exponential growth rates of their trajectories under three types of switching rules: arbitrary switching, optimal switching, and random switching. It is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong, the weak, and the mean generating functions, respectively. In particular, necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence. Various properties of the generating functions are established, and their relations are discussed. Algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples.