Researches On Stability Control Method Of Several Classes Of Switched Systems

Over the past ten years, the switching system as an important type of mixed system,attracted a large number of scholars to study. This is due to many physical processes of exchange and mixing are increasingly using computer to control, this exchange system displays the robot, mechanical systems, modeling and switching power converters gene regulatory networks and so on. However,it should be noted that due to the continuous dynamics and discrete dynamic interactions between the switching system can exhibit very complex dynamic behavior. For example, unfettered switch could shake a switching system,even if all subsystems are stable. Instead, you can set certain switching rules make the system stable, even if all subsystems are unstable. Therefore, it is difficult to study on the performance of switched systems, due to the hybrid nature of switching system operation, it has become a challenging problem.There are two main research content in the article, one is the two-dimensional system can switch by switching it has stability control methods; the second is to study the problem of fault-tolerant control Variable Delays switching system. Specific content is complete:The linear system theory and matrix inequality is applied in this article, by switching system equivalent transformation, determine whether the system can be stabilized by switching. First, the two-dimensional linear systems transform paper selected polar coordinate conversion, whereby the system variation distance and time to the origin and direction of motion systems and time variation, For any of the two-dimensional linear system according to the optimal method of fan is divided into areas with special properties, use these characteristics to features of regional, analyses how to design a suitable switching rate make the system stable. This paper developed the following two conclusions, firstly, when each subsystem is not stable, if it can develop a switching rule to stabilize the system, how to determine the switching rules; Second,when all of the subsystems are stable, select any of the switching rule whether the system will stabilize. Finally we got the standard to judge system stability.Secondly, This paper studies the variable delay switched system robust fault-tolerant control problem, the main way is applied Lyapunov stability theory, linear theory and LMI theory, when the system with a nonlinear term, uncertainties and actuator part failure, how to find the appropriate control design methods. In the actual project, part of the subsystem failure is common, would seriously affect the overall system, it is worth further study.