The Analysis And Synthesis Of Stability In Several Grey Systems

Grey control because of profound practical background has aroused widespread concern, and achieved fruitful research results. Stability is indispensable problems in the objective world and the engineering practical. It is an important attribute of the control system. Lyapunov method plays a vital role in the stability of the research. Based on the Lyapunov method the stability and the controller's design in several grey systems are studied, and the relevant criterions are obtained.First of all, the formation, research and one-dimensional feedback of grey system are recognized. The significance of stability in normal system is briefly introduced.And then, the stabilities of two special forms for dominant diagonal and symmetrical grey system should be understood. By a class of nonlinear disturbance of the grey continuous system, the consistent asymptotical stability and stabilization issues are discussed, and a method of robust stabilization control satisfying the conditions of Lipschitz is given. Using the nature of grey system itself, we provide the condition of consistent asymptotical stability, and design robust stabilization controller based on Lyapunov function and through practical examples of simulation correcting conclusions.Then, grey system will be introduced to the theory of nonlinear generalized system, based on the thinking of backstepping designing of a new grey sliding controller. There are not many strict restrictions for the selection of design parameters by this controller. The system can guarantee that the state was charged with rapid and robust stabilization and small overshoot. The method applied to a control system, the simulation results demonstrate that the proposed controller has superior performance.Finally, the grey system theory is introduced into the linear switching system. Single feedback control and more feedback control are designed respectively based on grey switching system. A single feedback control has the advantage of simple, while multiple feedback control can achieve stability when a single feedback can't reach, control respectively in the two examples are proved to be correct.