Output Feedback Control of Nonlinear Systems via Lipschitz Continuous Sliding Modes

This letter proposes a Lipschitz continuous output feedback sliding mode control law applicable to systems of arbitrary relative degree. The proposed controller compensates for non-vanishing perturbations with bounded time derivatives while ensuring finite-time stability of the origin. The finite-time stability of the closed-loop system is established using Lyapunov methods, leveraging the weighted homogeneity properties of both the controller and the observer. Furthermore, the observer and controller can be designed independently, thereby establishing a form of separation principle. The feasibility of the proposed method is demonstrated through simulation.