Novel Delay‐Dependent ℋ∞ 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 ℋ∞ control of Lur’e systems are considered. Using a convex representation of the nonlinearity, a novel delay‐dependent ℋ∞ 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 ℋ∞ 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 ℋ∞ norm constraint. Finally, two numerical examples show the effectiveness of the proposed method.