Robustness of exponential stability of a class of switched positive linear systems with time delays

• Published in: International journal of robust and nonlinear control Vol. 34; no. 4; pp. 2906 - 2926
• Main Authors: Son, Nguyen Khoa, Van Ngoc, Le
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.03.2024
• Subjects: Differential equations; Discrete time systems; Dwell time; Linear systems; Lower bounds; Perturbation; Robustness; robustness of stability; stability radius; structured perturbations; Subsystems; switched systems; Switching; time‐delay systems; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7115

Summary This paper investigates the robustness of exponential stability of a class of positive switched systems described by linear functional differential equations (FDE) under arbitrary switching or average dwell time switching. We will measure the stability robustness of such a system (which is considered as a nominal system) subject to parameter affine perturbations of its constituent subsystems matrices, by introducing the notion of structured stability radius. Some formulas for computing this radius, as well as estimating its lower bounds and upper bounds, are established. In the case of switched linear systems with multiple discrete time‐delays or/and distributed time‐delays, the obtained results yield tractably computable formulas or bounds for the stability radius. The extension of the obtained results to non‐positive systems and the class of multi‐perturbations has been presented. Examples are given to illustrate the proposed method.