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L2-gain analysis and feedback design for discontinuous time-delay systems based on functional differential inclusion

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3 Author(s)
Jiangyan Zhang ; Department of Engineering and Applied Sciences, Sophia University, Tokyo 102-8854, Japan ; Tielong Shen ; Xiaohong Jiao

A functional differential inclusion-based approach to L2-gain analysis and feedback control problems is presented for a class of discontinuous time-delay systems. Motivated by Filippov solution in the differential equations with discontinuous right-hand side, definition of the discontinuous time-delay systems forced by external signals is introduced, and a description of L2-gain property in the sense of the solution concept is given. Then, a condition such that a given discontinuous time-delay system has L2-gain less than a given level and the unforced system is stable in the sense of Filippov solution is presented based on a delay-dependent partial differential inequality. Furthermore, using the presented condition, a design method of state feedback controller is shown such that the closed-loop system satisfies the L2-gain constraint and asymptotical stability. Numerical examples are presented to demonstrate the presented theoretical results.

Published in:

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Date of Conference:

15-18 Dec. 2009