Variable Structure Control Of Discrete Uncertain Singular System With Time-days

With the development of new science and technology and needs of large engineering, uncertain singular systems with time-delay are put forward in many engineering fields. Because of the invariance of the sliding mode of the variable structure control system, in recent years, some researchers have studied variable structure control of singular systems and got some excellent results at home and abroad. However, the study of variable structure control of uncertain singular systems with time-delay, especially the study of variable structure control of discrete uncertain singular systems with time-delay has few results. So the study of variable structure control of discrete uncertain singular systems with time-delay is significant.In the thesis, by using the Lyapunov stability theory, the equivalent form of constrained system, variable structure control and the design of the switching function, the question of variable structure control of discrete singular systems, variable structure control of discrete uncertain singular systems with time-delay and variable structure control of discrete uncertain singular systems with multiple time-delays were studied. The main content is as follows.Firstly, the research background and significance of the variable structure control were introduced, and the present situation and present issues were described. Then some basic knowledge of singular systems and variable structure control is introduced and the lemmas used in this thesis were summarized.Secondly, the variable structure control problems for discrete uncertain singular systems and discrete uncertain singular systems with time-delay were discussed separately, then the methods of the front system were applied to variable structure control of discrete uncertain singular systems with multiple time-delays. A switching function with a difference compensator and a variable structure controller is designed, which eliminated the limitation of uncertainties which must be bounded and not satisfy matching conditions. The design of variable structure control not only weakened the chattering effectively, but also improved the dynamic quality.Thirdly, the variable structure control problems for a class of time-delay discrete uncertain singular systems with structured perturbation were studied. A new switching function with a difference compensator is designed, which guarantees that movement of the system is asymptotically stable in a quasi-switching manifold, then a variable structure controller is designed, which can force the system trajectory to enter into a small neighborhood of the quasi-switching manifold in limited steps and be convergent to a small chattering in the neighborhood. Finally, a numerical example was given to demonstrate the effectiveness and practicability of the design method.Finally, a conclusion is given to summarize this thesis, the prospect of further study on the theory of discrete uncertain singular system with time-delay is presented.