Design of variable structure controller for uncertain time-delay singular system

To study the approximation theory of real sliding mode and the design of variable structure controller for time-invariant linear uncertain time-delay singular system, the approximation theory of real sliding mode was developed to provide foundation for obtaining sliding mode by equivalent control, and switching functions with integral dynamic compensators and variable structure controllers were designed respectively under two circumstances that the system without uncertain part was stabilized by delay-dependent and delay-independent linear state feedback. The design guarantees the asymptotical stablity of switching manifolds, and the variable structure controllers can force solution trajectory of the system to arrive at the switching manifolds in limited time. A numerical example is given to demonstrate the feasibility and simplicity of the design method.