Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure

Ji-Shi Zhang, Yan-Wu Wang, Jiang-Wen Xiao and Yang Chen

International Journal of Systems Science, 2016, vol. 47, issue 4, 946-955

Abstract: This paper addresses the robust reliable guaranteed cost control problem of positive interval systems with multiple time delays and actuator failure for a given quadratic cost function. Through constructing a Lyapunov–Krasovskii functional, a sufficient condition for the existence of robust reliable guaranteed cost controllers is established such that the closed-loop system is positive and asymptotically stable, and the cost function is guaranteed to be no more than a certain upper bound. Based on the linear matrix inequality method, a criterion for the design of robust reliable guaranteed cost controllers is derived which can tolerate all admissible uncertainties as well as actuator failure. Moreover, a convex optimisation problem with linear matrix inequality constraints is formulated to design the optimal robust reliable guaranteed cost controller which minimises the upper bound of the closed-loop system cost. A numerical example is given to show the effectiveness of the proposed methods.

Date: 2016
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DOI: 10.1080/00207721.2014.911382

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