H∞ observer-based sliding mode control for uncertain discrete-time singularly perturbed systems

This paper studies the sliding mode control (SMC) problem of discrete-time singularly perturbed systems (DTSPSs) with external perturbations and nonlinear inputs. First, to estimate the state of the original system, a novel state observer is constructed. Under this condition, the observer error system is ensured to be input-to-state stable (ISS) and satisfies the given H∞ performance index. Then, an appropriate sliding mode control law is proposed to satisfy the reachability condition. On this basis, the ISS criterion for the sliding mode dynamics (SMDs) is given, and the controller gain matrix is also obtained. In addition, a feasible algorithm is given to compute the upper bound for the small parameter. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.