State and output feedback H∞ control of time-delay switched linear systems

• Published in: International journal of robust and nonlinear control Vol. 22; no. 15; pp. 1674 - 1690
• Main Authors: Galbusera, Luca, Bolzern, Paolo, Deaecto, Grace S., Geromel, José C.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.10.2012; Wiley Subscription Services, Inc
• Subjects: H∞ control; linear matrix inequality; output feedback; stabilization; switched systems; time-delay
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.1777

SUMMARY In this paper, we propose contributions on the stabilization and H∞ control of switched linear systems subject to time‐delays through the assignment of the switching law. As a first step, based on previous results related to switched linear systems with no time‐delays and exploiting the concept of piecewise quadratic Lyapunov–Krasovskii functionals, we solve the problem of finding suitable state‐dependent switching laws ensuring the prescribed control objectives. Secondly, we extend such results and present a strategy to construct an output feedback switching law, based on the available measurements made on the system. In both cases, the design of the control strategy is done by computing a feasible solution to a set of matrix inequalities associated to the modes of the switched linear system. Copyright © 2011 John Wiley & Sons, Ltd.