An LMI-Based Stabilization Criterion of Sliding Mode Control for a Class of Bilinear State-Delay Systems

This paper focuses on the problem of sliding mode control for delay-dependent stabilization criterion of bilinear state-delay systems. Based on the linear matrix inequality (LMI) method and a parameterized model transformation technique, we provide a sufficient condition for the existence of sliding surface and we give an explicit formula of sliding surface guaranteeing the asymptotic stability of the reduced-order equivalent system dynamics restricted to the sliding surface. The proposed stabilization criterion can also be applied to control the bilinear systems with time-varying delay. Finally, a simulation study shows that our method is effective and useful. Keywords—sliding mode control, delay-dependent stabilization criterion, bilinear state-delay systems, parameterized model transformation, sliding surface.