Sliding mode control design for uncertain discrete-time systems

The design of sliding mode schemes for uncertain discrete-time systems is considered. Previous work which attempts a parallel approach to that used for the continuous case is reviewed. A novel philosophy and methodology for the design of discrete-time sliding mode control systems using known results from uncertain systems theory are presented. It is clearly demonstrated that it may not be appropriate to choose the sliding surfaces to discrete-time control systems using the continuous-time methodology. A numerical example reflecting an actual design problem in the area of robust control of an industrial furnace is considered to illustrate the results obtained. Simulation results demonstrate that a simple linear control structure coupled with a hyperplane designed using the results presented will provide equivalent performance to that of an involved nonlinear control configuration and an associated sliding subspace which does not satisfy the criteria presented