Stability Analysis And Control Of Linear Parameter-varying Systems With Time Delay And Saturation

Time delay and saturation are widely exist in control system, such as mechanicaldriven system, network control system, chemical system and so on. If we ignore theirinfluence in the process of analysis and design, the system performance may bedegraded, in severe cases, it may lead to the system instability. Time delay systems withsaturation, which is considered to be one of the most difficult to control, have importanttheoretical research value and practical significance, also have made a lot of researchresults in recent years. In addition, since linear parameter varying model can be used torepresent many engineering problems, such as variable pitch wind power generationsystem, aircraft systems, etc., the researches on linear parameter varying (LPV) systemare equally important. Based on the review of previous research work, a thoroughdiscussion about the questions of stability analysis, stabilization and Hinf controllerdesign for time delay LPV systems are carried in this thesis.We study the stability analysis problem of time LPV system. A sufficient conditionfor stability is come up with by using the idea of delay partition, Jensen’s integralinequality and the nature of integral. In order to facilitate solving, results are presentedin the form of LMI. It is the basic theory for study the stabilization and Hinf controlproblems.Combining with the above research results, we discussed the stabilization controlproblems for time delay saturation linear systems and time delay LPV systems.Parameterized controllers are given in the form of linear matrix inequalities respectively,and can be easily tested by MATLAB LMI toolbox. Appropriate numerical examplesare given to compare with other scholar’s results. The results show that the controllerdesigned by our methods can achieve better control effect and less conservatism.For the purpose of analysis the capacity of resisting disturbance of the system, wealso consider the Hinf performance analysis and controller design problems for timedelay saturation LPV system. More specifically, the result of stability analysis is thebasis of the problem of Hinf performance analysis. Sufficient conditions are derived forensuring the stability of the LPV system with a prescribed Hinf norm bound whenthere exist energy bounded external disturbance. Design problem is to deduce a statefeedback controller which guaranteed the stability of the system in the domain ofattraction and satisfy a certain level of Hinf disturbance attenuation. The problem ofdetermine the upper bound of is converted into a convex optimization problem.