Study On Guaranteed Cost Control For Uncertain Nonlinear Time-Delay Systems Via LMI Approach

Time delay is a common phenomenon in industries. Many practical processes include time delays in their dynamic equations, such as biology, chemistry, economy, mechanism, physics, physiology, population and engineering etc. For one thing, because of the executing time of actuator and sensor and the time of network communications, there are also time delays in the closed-loop systems, such as network control system etc. On the other hand, the characteristic equations of the controlled systems with time delays are transcendental equations and belong to infinite dimensional systems, so it is difficult to study the time delay systems in mathematics theory and also difficult to obtain good performance for the time delay systems using the controller designed by classical control theory. So study for the time delay systems is significant both in theoretical and practical field.Most of the time, it is hard to obtain the exact model of the controlled plant in practical systems, and sometimes we have to simplify the model for its complexity even if we get the exact model of the controlled plant. Besides the imprecise model, the character of the controlled plant also changes when the work condition and environment change or the gains of the system components change by aging, so it has errors with the standard characteristic of the plant and the uncertainties are occurred.With the development of technology, people are stricter with the analytical requirement in the practical industrial process. More and more analytical scientific experiment proves: any practical physical system is a kind of nonlinear system andlinear system is just a kind of approximate description. So it's more significant to research nonlinear system.Recently, more and more attention has been paid to the problem of designing robust controllers to make uncertain systems not only are stable but also guaranteed an adequate level of performance. Fortunately, one approach to this problem is the guaranteed cost control approach introduced by Chang and Peng firstly. This approach is to design a controller so that the closed-loop system is asymptotically stable for all admissible uncertainties and the closed-loop cost function value is not beyond a specified upper bound. Therefore, there has been a increasing interest in the guaranteed cost control of uncertain time-delay systems and many significant results have been presented in the past years. However, there have been few results for nonlinear systems.Most of the time, there is an assumption during the process of the controller design, known as the controller can be achieved accurately. Actually in terms of the constraints of technical level during the realization of the controller, as well as the system component aging, the controller parameter is determined to change,such as the constraints of computer word length and the inherent error of the signal conversion between analog and data. The existing robust controller method pays much attention to the uncertainty of parameter, while ignoring the controller gain. In this paper, the problem of the non-fragile guaranteed cost control has been studied when it have additive and multiplicative disturbance of the controller.Based on Lyapunov stability theory and linear matrix inequality approach, the problems of guaranteed cost control for nonlinear time-delay systems with norm-bounded uncertainties are considered. The main contents in this paper are as follows:(1) For its efficiency of solving nonlinear systems, T-S model and its corresponding control methods have been used greatly to analyze and synthesize nonlinear systems recently. The guaranteed cost control problem for uncertain nonlinear time-delay systems with delay-independent and delay-dependent is considered respectively in this paper. Several criteria for the existence of theguaranteed cost control law and design method are given though solving LMIS. An upper bound on the guaranteed cost is also minimized by solving a convex optimization problem.(2) On the assumption of the nonlinear part is also a method to solve the nonlinear system. Furthermore, for most of the modern results, although the controllers given by using the existed methods are robust regard to system uncertainties, the robustness of controller uncertainties has not been considered. The controller may be sensitive or fragile when considering the perturbations in the controller coefficients. The non-fragile guaranteed cost control problem is discussed for uncertain nonlinear time-delay systems under two classed of controller gain perturbations in this paper, using the LMI method. The two controller gain perturbations are additive form and multiplicative form. The sufficient conditions of the non-fragile guaranteed cost controller are giver in terms of LMI. The optimal guaranteed cost value of the system is given through solving a convex optimization problem.