A practical method for the design of sliding mode controllers using linear matrix inequalities

This paper considers the problem of selecting a sliding surface for a given system in an optimal way such that the performance of the reduced order system is balanced against the control costs required to maintain sliding. This approach is quite different from many of the existing schemes in the literature, in which no direct account is taken of the control effort. Two new numerical schemes are presented both involving convex optimization problems. Two simple examples are given to demonstrate the theory.