DIFFERENCE EQUATION MODELING OF A VARIABLE-STRUCTURE SYSTEM

Variable structure systems with sliding modes have been widely discussed and used in many different fields of applications. The precise behaviour at a switching surface is complicated because there the system is nonanalytic. A two-dimensional variable structure system is analysed in detail using a special discretisation with a difference equation model which is best in a particular sense. This reveals the occurrence and structure of discrete pseudo-sliding modes, which give insight to the corresponding sliding modes for the continuous system. Necessary.and sufficient conditions are obtained for the occurrence of the pseudo-sliding modes and the analysis illustrated with graphs from numerical solutions.