Guaranteed cost control for uncertain non-linear systems with time-varying delays using T–S fuzzy model

This paper investigates the guaranteed cost control problem of uncertain non-linear systems with time-varying delays via the Takagi–Sugeno fuzzy model approach. Based on the Lyapunov–Krasovskii functional theory and the linear matrix inequality technique, a state feedback controller is proposed to stabilise the non-linear systems and minimise the guaranteed cost of the closed-loop systems. Both delay-dependent and delay-independent stability criteria are derived to guarantee the asymptotic stability of closed-loop systems. Furthermore, the supplementary requirement that the time-derivative of time-varying delays must be smaller than one is released for the proposed delay-dependent stability criterion. Two illustrative examples are provided to verify the validity of the results developed in this paper.

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