摘要：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.

摘要：A designing method is presented to find stabilizing saturated linear controllers for linear continuous time and discrete time singular systems with control constraints. The idea is as follows: The system is first stabilized by a low-gain linear state feedback control. A general Lyapunov function is found, on the basis of which another linear state feedback control is computed. The second step is very similar to a relay control design. The two controls are added and saturated.