An improved stability result for linear time-delay system using a new Lyapunov–Krasovskii functional and extended reciprocally convex inequality

ABSTRACT This paper is concerned with the stability analysis of a linear system with interval time-varying delay using an augmented Lyapunov–Krasovskii (LK) functional approach. A delay-dependent stability criterion is developed in LMI framework to estimate the maximum allowable bound of the time-delay within which the system remains asymptotically stable in the sense of Lyapunov. Conservatism in the proposed delay-dependent stability analysis is reduced by introducing a new LK functional along with the Wirtinger's inequality and extended reciprocally convex matrix inequality. Finally, two numerical examples and the load frequency control problem have been solved to validate the superiority of the proposed stability criterion compared to existing literature.

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