Dynamic sliding mode control for nonlinear parameter-varying systems

This article deals with the dynamic sliding mode control (SMC) problem for unmatched nonlinear parameter-varying systems. The unmatched nonlinear model refers to the systems matrices of control input and nonlinearity terms having inconsistent values and structures. A linear sliding surface function is constructed, and the resulting sliding mode dynamics is formulated into a full-order descriptor nonlinear parameter-varying system. Then, based on a parameter-dependent Lyapunov function, the synthesis procedure of the sliding manifold is derived, which guarantees the asymptotic stability of the sliding motion. Furthermore, a dynamic SMC law is proposed to enforce the resultant closed-loop system towards the sliding manifold in finite time. It is noteworthy that both the sliding surface and control law are depended on both time-varying and measurable parameters. Finally, simulation studies are provided to unfold the validity of the proposed method.