Novel Delay-Dependent Stabilization Criterion for Lur’e Systems with Sector-Restricted Nonlinearities and External Disturbances via PD Feedback Approach

In this paper, the effects of time delay on control of Lur’e systems are considered. Using a convex representation of the nonlinearity, a novel delay-dependent stability criterion is derived for the Lur’e systems via proportional-derivative (PD) feedback law. The Lyapunov–Krasovskii functional based on the delay discretization approach is used for the purpose of obtaining the stability condition by utilizing Projection Lemma. The criterion is utilized to not only guarantee stability of systems but also reduce the effect of external disturbance to an norm constraint. Finally, two numerical examples show the effectiveness of the proposed method.

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