Variable structures control for time-varying nonlinear time-delay singular system

Synthesis and design of variable structure controller for time-varying nonlinear time-delay singular system with fixed structure are studied. Firstly, a new restricted system equivalent form is developed. The system is decomposed into two lower dimension subsystems: one is a normal time-varying nonlinear differential difference system without input, another is a time-varying nonlinear difference system with input. Secondly, In view of two cases that the nonlinear part of the system satisfies matching conditions and the nonlinear part of the system dissatisfies matching conditions, switching functions with integral dynamic compensator and variable structure controllers are designed respectively, which guarantee that the sliding modes are asymptotically stable and the variable structure controllers can force solution trajectory of the system to arrive at the switching manifold in limited time. Finally, a numerical example is given to demonstrate feasibility and simplicity of the design method.