Discrete variable structure control systems

Abstract We discretize n-th order linear systems with variable structure control under a particular discretisation scheme and analyse these systems in detail. The occurrence and structure of pseudo-sliding modes give insight into the corresponding sliding modes for continuous systems, and enable the relation between the system parameters and the stepsize to be explored. By means of constructing asymptote hyperplanes on which the system trajectories diverge, an algorithm is developed that calculates an upper bound of stepsize, within which the system will remain in a neighbourhood of switching hyperplanes. A sufficient condition for the existence of pseudo-sliding mode is derived. This discretisation helps one to understand the inherent properties of computer controlled variable structure control systems. The analysis is illustrated with simulation studies of second and third-order systems.