Study And Application On Model Reduction And Stability For Controlled Systems

An important thought of control theory is to establish a mathematical model by a differential equation for the controlled object and then analysis and synthesis the mathematical model. On the one hand, the mathematical model of the controlled object was obtained through the system analysis and modeling, and gotten by the parameter identification method. With the development of modern control system more complex and large-scale, the dimension of mathematical model is also more and more high. On the other hand, the order of the controller is often the same as the controlled system in the application of modern control theory such as H∞, H2,μanalysis and synthesis. It caused a lot of trouble in engineering practice. such as the desired cost is higher and the complex degree is large. While the lower order means that a simple simulation program, less computer time, less dynamic components, the lower noise sensitivity, and the high reliability design, simulation and realization of system. Researchers often hope that the order number of controlled system cannot be too large in order to research and analysis of convenience in the control engineering. Therefore, model order reduction has a wide range of demand and application. Many systems are also always affected by a variety of interference. Stability is the premise of reduced order model. So, the stability is of great significance. First of all, the exponential stability and adaptive synchronization of system were studied in the thesis. And then the problem of model order reduction were discussed for the stochastic uncertain system, the distillation tower linear system and the controlled Hamiltonian system.The main achievements of this dissertation are as follows.(1) We have dealt with the problem of the mode and delay-dependent adap-tive exponential synchronization in pth moment for neural networks with stochas-tic delayed and Markovian jumping parameters. We have removed the tradi-tional monotonicity and smoothness assumptions on the activation function. A M-matrix approach has been developed to solve the problem addressed. The con-ditions for the adaptive exponential synchronization in pth moment have been derived in terms of some algebraical inequalities. These synchronization con-ditions arc much different to those of linear matrix inequality (LMI). Via the adaptive feedback control techniques, some suitable parameters update laws arc found.(2) The problem of robust H∞model reduction for uncertain stochastic systems with time-delay is investigated. For a given stable system, our attention is focused on the construction of reduced-order models which guarantees the corresponding error system to be asymptotically stable and has a prescribed H∞error performance. Some sufficient conditions are obtained for the existence of solutions for time-delay dependent problems in terms of certain LMIs and a coupling nonconvex rank constraint condition. Desired reduced-order model can be constructed when these conditions are satisfied.(3) The problem of robust H∞model reduction for neutral type control system with time-delay is investigated. A sufficient condition is proposed for the asymptotic stability with an H∞error performance for the error system. Then, the H∞model approximation problem is solved by using the projection approach, which casts the model approximation subject to LMI constraints by employing the cone complementary linearization algorithm.(4) The method of this dissertation is applied to a class of distillation linear system and controlled Hamiltonian system. First of all, the distillation column and controlled Hamiltonian linear systems are described. On this basis, the H∞model approximation problem is solved by using the projection approach.