Optimal discrete sliding mode control with application

Presented is a study of a design methodology for sliding surfaces for single-input discrete-time sliding-mode control systems. A viable robust algorithm is detailed. The primary result is the optimal design of discrete-time sliding surfaces with respect to a linear-quadratic criterion. This case is considered for both the cheap control and general versions. The cheap control formulation results in an explicit sliding surface, whereas the general case requires an iterative solution. The control system is applied to a pulse-width-modulated gantry crane problem, showing the effectiveness of the design method