A class of discrete variable structure systems

A class of nth-order linear systems with a variable structure is discretized and analyzed in detail. The occurrence and structure of pseudo-sliding modes give insight into corresponding sliding modes for the continuous system, and enable the relation between system parameters and the step size to be explored. A discretization can be used which gives a mathematical model revealing details of the chattering along a surface. A sufficient condition on the step size and the system and switching parameters to ensure the existence of a pseudo-sliding mode is derived. The analysis is illustrated with a simulation study of second-order systems