Decentralized Nonfragile Guarranteed Cost Control Of A Class Of Interconnected Composite Systems

Control analysis of interconnected composite systems has long been a main and difficult issue in control area. Control of interconnected composite systems can be divided into two main strategies: decentralized control and centralized control. Centralized control fits a relatively small area due to its need of all subsystems' information. While decentralized control can simplify control problem of composite systems into control problem of several subsystems with lower dimensions, thus generates easier controller. So it gains much more attention.When implementing control and design for systems, we wish the controllers we designed not only make the system asymptotically stable, but also make the system satisfying some performance index. This kind of control problem is the so-called guaranteed cost control problem. This control strategy has run through many aspects of control area.When studying control problems, people usually take only the system uncertainty itself into account, and hope that the desined controller could exactly achieve the control task people expected. In fact, since the implement of controller is affected by hardware, software, arithmetic, and so on, the controller itself may contain certain uncertainties, which may degrade system performance and/or destroy system stability. So, when designing controller, we should consider not only system uncertainty, but also the impact of disturbance of the controll itself. This leads to the so-called nonfragile control problem, which gains more and more attention.Much work has been done in research of guaranteed cost control of interconnected composite systems. Research on nonfragile guaranteed cost control of single nonlinear system and nonfragile guaranteed cost control of linear interconnected composite systems has also been done by several researchers. But up to now little has been reported on the research concerning nonfragile guaranteed cost control of nonlinear interconnected composite systems.In this thesis we do an elementary research on nonfragile guaranteed cost control of nonlinear interconnected composite systems. The main work can be concluded as:Firstly, for a class of nonlinear interconnected composite systems, in cases when the controller parameter disturbance are of additive form and multiplicative form, respectively, by using Lyapunov stability theory, combined with linear matrix inequality technology, we presented a sufficient condition on the existance of decentralized nonfragile guaranteed cost controller, and offered a designing method to the controller. Finally, we proposed an arithmetic on constructing optimal decentralized nonfragile guaranteed cost controller through a convex optimization problem.Secondly, we tested the corresponding arithmetic by a numerical example.