Variable Structure Control Of Time-delay Singular Systems

The dissertation focuses on studying variable structure control of continuous and discrete time time-delay singular systems.1. Variable structure control of continuous time-delay singular systems(1) Theory and designing of variable structure controller for time-invariant linear uncertain time-delay singular system are studied. Firstly, approximation theory of real sliding mode is developed. Secondly, necessary and sufficient conditions on invariant of sliding mode are given. Thirdly, designing of variable structure controller for a class of time-invariant linear uncertain time-delay singular system is discussed. Lastly, a numerical example is given to demonstrate the feasibility and simplicity of the design method.(2) Synthesis and designing of variable structure controller for time-variant linear time-delay singular system with fixed structure are studied. Firstly, a new restricted system equivalent form is developed and the system is decomposed into two low dimensional subsystems: one is a normal time-variant linear differential difference system without input; another is a time-variant linear difference system with input. Secondly, based on some results on asymptotic stability of time-delay singular systems, switching function with integral compensator is designed and sufficient conditions on asymptotic stability of the sliding mode are given. Thirdly, variable structure controller is designed, which guarantee the solution trajectory of the system arrive at the sliding manifold in finite time. Finally, a numerical example is given to demonstrate feasibility of the design method.(3) Synthesis and designing of variable structure controller for time-variant nonlinear time-delay singular system with fixed structure are studied. Firstly, in terms of whether the nonlinear part satisfies matching conditions or not, the system is decomposed into two different systems. Secondly, different switching functions with integral compensator and variable structure controllers are designed respectively for the two systems, which guarantee the closed-loop systems are globally asymptotically stable. Finally, a numerical example is given to demonstrate feasibility of the design method.(4) Synthesis of variable structure controller for time-invariant time-delay singular uncertain systems with structural disturbance and nonstructural disturbance are studied. Different switching functions with integral compensator and variable structure controllers are designed respectively and, numerical examples are given to demonstrate the feasibility of the design methods.(5) Synthesis of output variable structure controller for time-invariant linear time-delay singular system is studied. According to different cases of eigenvalues of the system without time-delay, switching function with integral compensator and variable structure controller are designed respectively by using the output...