Sliding-mode control for uncertain neutral delay systems

The problem of sliding-mode control for a class of neutral delay systems with uncertainties in both the state matrices and the input matrix is considered. By selecting a sliding surface depending on the current state and delayed state, the paper gives a sufficient condition in terms of linear matrix inequalities (LMIs) such that the closed-loop system is guaranteed to be asymptotically stable. When LMIs are feasible, the design of the sliding surface and the sliding-mode control law can be easily obtained by convex optimisation. State trajectories are attracted onto the sliding surface in a finite time and remain there for all subsequent time. A simulation illustrates the application of the method.