| The control problems for time-varying systems are a difficulty all along. To a time-varying system, a Riccati equation or a Lyapunov equation will be performed when a controller designed. As it is difficult to solve a nonlinear equation and can not obtain an analytic result, the control problems for time-varying system are usually ignored. But a large of control plants is time-varying systems in control engineering; the study of time-varying systems must be a promising future.It is well known that switching systems usually contact with Multi-model systems, and the control problems for Multi-model is more complicated than for single model. To a certain extent, the combination of the switching control theories with other control technology solved Multi-model control problems had already achieved high success. Such as in the field of the adaptive control, the Multi-model systems with large uncertainties have been solved according to definition of switching conditions , design of switching strategies. But in a sense, time-varying systems are equal to Multi-model systems because of Multi-model in time-varying systems. This gives us enlightenment that whether switching control theories may solve the control problems for time-varying systems.According to perturbation and robust bounds in the robust control theories, the author designs a new control algorithm, which divides time-varying systems into some sections. In every section, time-varying model is composed of the nominal model and perturbation, and the controller according to the nominal model applies in time-varying system. So control algorithm not only makes the nominal model stable asymptotically, but also makes the time-varying system stable asymptotically. In the end, took advantage of switching between models with models, we achieve the object that make the time-varying system controlled. Simulations show the effectiveness of the algorithm and can avoid the difficulties in a Riccati equation or a Lyapunov equation solved.
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