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.