Robust Sliding Mode Control for a Class of Nonlinear Uncertain Neutral Systems

This paper aims to investigate the robust sliding mode control problem for a class of nonlinear uncertain neutral systems. For such systems, we derive sufficient conditions for asymptotic stability of the closed-loop system by selecting sliding surfaces that depend on both current states and delayed states. The analytical approach is based on linear matrix inequalities (LMIs), and a novel control algorithm is proposed. Specifically, the system is decomposed into multiple subsystems, with each subsystem controlled independently. Different control strategies can be applied to individual subsystems to achieve optimal overall system performance. The implementation involves designing switching functions using state feedback matrices obtained from LMI solutions, where MATLAB's "feasp" solver or equivalent convex optimization tools can be employed to verify feasibility. This method effectively enhances system robustness and stability, meeting practical application requirements through distributed control architecture and LMI-based stability verification.