Linear Matrix Inequalities in Robust Unified Smooth Sliding Mode Controller Design

A wide range of problems encountered in system control theory can be reduced to a few standard convex or quasiconvex optimisation problems involving linear matrix inequalities (LMI). With recent developed of interior point methods, the optimisation problems can be solved numerically very efficiently. One of the applications of the LMI may be seen in solving the sliding mode control problems. The sliding mode control system is capable of total invariance to the matched uncertainties while remain in the sliding mode. But the system may still face the undesirable distractions cause by the mismatched uncertainties, and chattering problem. In this paper, the sliding surface is designed with integration of an optimal guaranteed cost H infinity criterion to attenuate the mismatched disturbances. The guaranteed cost surface is derived from a convex optimisation procedure formulated as an LMI problem. A unified smooth control law is applied to solve the chattering problem. The results showed that the controller may improve the performance with total chattering elimination and mismatched disturbances rejection