Approximation Theory of Real Sliding Mode in Variable Structure Control of Time-Delay Singular System

Theory of approximation between real sliding mode and ideal sliding mode in variable structure control of linear time-delay singular uncertain system is studied. According to the theory, it is need only to study the ideal sliding mode in order to guarantee the system possess of good transient performances. The theory is natural generalization and improvement of those in normal systems, time-delay systems and singular systems.