A Delay-Dependent Approach to Finite-Time H∞ Control of Nonlinear Descriptor Systems with State Delay via Observer-Based Control

This paper proposes a finite-time observer-based controller for time-delay descriptor systems with time-varying disturbances, model uncertainties, and one-sided Lipschitz nonlinearities. For this purpose, first, a nonlinear descriptor observer is designed, and the observer error system is calculated. Then, the observer-based control law is proposed to provide the conditions for robust stabilization of the closed-loop descriptor system by selecting an appropriate Lyapunov–Krasovskii functional. According to the delay-dependent stability criterion, LMI-based sufficient conditions are derived and the gains of the controller and the observer are calculated. The proposed controller guarantees the finite-time boundedness and H∞ disturbance attenuation of the closed-loop descriptor system. Finally, the effectiveness of the proposed technique is investigated through computer simulations.