LMI-Based Approaches To Non-fragile Control For Nonlinear Systems

With the rapid development of the scientific technology, the scale of the industrial control systems are more and more complex, many complex practical engineering sys-tems including chemical industry, metallurgy, machinery, electricity, communications, aerospace, etc, are all with nonlinear property, and the accurate mathematical model are very difficult to be obtained or even cannot be obtained. So, the study of nonlinear con-trol systems has become one of the hot problems. Under the premise that it is difficult to obtain accurate mathematical model, how to solve the control problem of nonlinear systems is a complex and interesting subject. And how to characterize the nonlinear characteristic is the key problem of studying such systems. In this paper, two different types of nonlinear systems including nonlinear systems with sector bounded and fuzzy nonlinear systems are employed to study the control problem of nonlinear systems. On the other hand, due to the increasing demand for industrial efficiency, digital computer technology has been rapid development. And the research on the digital control system has become an important direction in the control theory and practical application. Most modern and advanced control systems are digital, and usually realized by such as digital signal processors (DSP) or general-purpose microprocessors and other computer devices. This greatly improves the efficiency of industrial processes, and further improves the pro-duction efficiency. However, an problem cannot be ignored for digital control system is that there are some inevitable uncertainty in the controller. As shown in many literatures, in the process of the controller design, very small controller gain variations can lead to the closed-loop performance degradation and even unstable. Therefore, how to design a filter or controller so that it is not sensitive to parameters perturbations is an important issue.Motivated by the above reasons, this thesis, based on previous works of others, focuses on the non-fragile problem of controllers/filters for two classes of nonlinear systems. On one hand, for a class of nonlinear discrete-time systems with sector-bounded nonlinearities, proposes a new type of filter/controller parameter perturbations with smaller conservativeness and further studies the problem of non-fragile dissipative filter/controller design. On the other hand, for the fuzzy nonlinear systems, we study the fuzzy non-fragile filter and controller design problems, respectively. The designed filters/controllers are considered with interval gain variations. And a structured vertex separator approach is employed to solve the mathematical computational problem caused by the interval gain variations. And examples are given to illustrate the superiority and efficiency of the proposed methodsThe main contributions are as follows:Chapters1-2first summarize and analyze the development and main research meth-ods in non-fragile control problem for nonlinear systems. Preliminaries about the consid-ered problem are also given.Chapter3investigates the problem of non-fragile dissipative filtering for a class of nonlinear discrete-time systems with sector-bounded nonlinearities based on linear matrix inequality (LMI) technique. The filter under study is subject to a new type of multiplica-tive gain variations, which can reduce the conservativeness. S-procedure approach is proposed to solve the sector-bounded nonlinearities. Furthermore, a sufficient condition for the existence of the non-fragile strictly (Q, S, R)-dissipative filter is obtained by us-ing linear matrix inequality (LMI) techniques. The theoretical and simulation prove the effectiveness of the proposed method.Chapter4studies the problem of non-fragile nonlinear memory state feedback H∞controller design for a class of discrete-time systems with simultaneous sector-bounded nonlinearities and varying time delay, a sufficient condition for the existence of the non-fragile H∞filter is obtained by using linear matrix inequality (LMI) techniques. The pro-posed method has less conservative in theory. Simulation example further demonstrates the superiority of the new method.Chapter5focus on the fuzzy non-fragile H∞filter design problem with the consid-eration of the interval type of gain variations for fuzzy nonlinear systems. The structured vertex separator is employed to solve the numerical computational problem caused by the interval type of gain variations successfully. LMI-based sufficient conditions are proposed for the fuzzy non-fragile H∞filter design, and we have proved in theory and simulation that the proposed method is with less conservative than the existing method with the con-sideration of the norm-bounded type of gain variations.Chapter6studies the problem of the fuzzy non-fragile dynamic output feedback H∞controllers design for fuzzy nonlinear discrete-time systems. The same with Chapter5is that the structured vertex separator is employed to solve the numerical computation problem caused by interval gain variations. By using the LMI technique, a two-step algo-rithm is proposed to give the sufficient condition for the fuzzy non-fragile dynamic output feedback H∞controllers design. Similarly, we have proved in theory that the proposed method is with less conservative than the existing method. And finally, the numerical example has shown the effectiveness and the superiority of the proposed approach.Finally, the results of the dissertation are summarized and further research topics are pointed out in Chapter7.