Research On Analysis And Control Of Uncertain Stochastic Time-delay Systems

Stochastic phenomena are ubiquitous natural phenomena in the natural world. In nature, social economy, and practical engineering, the dynamic rule of many problems can by described by deterministic system model and stochastic system model. In ideal condition, the system is often simplified into the deterministic system model, which is convenient for analysis and synthesis. Along with the rapid development of science and technology, the actual engineering technology to the accuracy requirement of the system is getting higher and higher. The original simplified deterministic system model can not meet the accuracy requirements of the practical engineering. So it is necessary to consider the influence of the stochastic factors, use stochastic model to establish mathematical model, and use the stochastic point of view to analyse and synthesize the system. In recent years, the study of analysis and synthesis of stochastic system has become a popular issue in the field of control theory.Based on the state space, accurate mathematical model is used to design and analyse the control system in the modern control theory. The controlled system is often impacted by parameter error, unmodeled dynamics and uncertain external disturbances, which cause the system uncertainty. The uncertainty of the system can lead to the control system out of control and not reach the expected performance index. The study on the influence of uncertainty for system performance produces robust control theory. On the other hand, time-delay can not be avoided, which is often the source of instability and poor performance in many practial systems. Therefore, it is of great theoretical significance and application value to study the robust stability and control problems of uncertain time-delay stochastic systems. By using Lyapunov-Krasovskii functional, It o stochastic formula, delay partitioning, together with Schur complement lemma and linear matrix inequality, this thesis focuses on the delay-dependent robust stability analysis, robust H∞control, robust non-fragile H∞control and passive control of linear or nonlinear uncertain stochastic time-delay systems.The main contents and contributions of this dissertation are summarized as follows:When the stochastic disturbance is zero, uncertain stochastic time-delay systems are reduced to uncertain time-delay systems. Based on the new integral inequality, that is deduced by Jensen inequality, new delay-dependent sufficient criteria of uncertain time-delay systems are derived. By introducing appropriate number of free-weighting matrix, new integral inequality is established and the integral inequality approach is extended to stochastic systems. Using new integral inequality and delay partitioning, the delay-dependent stability criteria of linear or nonlinear uncertain stochastic time-delay systems are obtained, which avoid model transformation and bounding techniques for cross terms. While dealing with the nonlinear perturbation which satisfies linear growth condition, the matrix inequality condition is removed by using the trace characteristic of matrix, such that the result is less conservative. Numerical examples are given to illustrate the effectiveness and less conservativeness of the proposed method.Based on the method of the new integral inequality and delay partitioning, the robust H∞control problem for uncertain stochastic time-delay systems in state and control input is investigated. The time delay is assumed to be a time-varying continuous function varying in an interval. The delay-dependent sufficient criteria of stochastic stabilization and robust H∞control for the systems are presented in terms of LMIs. One of the important features of the results is that the conservatism reduction becomes more obvious as the delay decomposing number increases, which will be illustrated via numerical examples.By splitting the delay into two sections and constructing appropriate Lyapunov-Krasovskii functional, the stochastic bounded real lemma of nonlinear uncertain stochastic time-delay systems is presented. Combing the lemma with linear matrix inequality, the robust H∞control problem for nonlinear uncertain stochastic time-delay systems is discussed. And the state feedback robust H∞controller is designed. The developed results have advantages over some previous ones, in that they involve fewer matrix variables but have less conservatism and they also enlarge the application scope. Numerical examples show the effectiveness of designed controller.The problem of roubst non-fragile H∞control for nonlinear uncertain stochastic time-delay systems is considered. Based on appropriate Lyapunov-Krasovskii functional and free-weighting matrix method, the non-fragile H∞controller is designed. The designed controller can ensure that the closed-loop system is robustly stochastically stable and a prescribed H∞performance is required to be satisfied, even if there are errors in the controller coefficients. The sufficient condition for the existence of the non-fragile H∞controller is delay-dependent, which is less conservative than delay-independent one. The upper bound of the delay derivative is allowed to be greater than or equal to one, the limit of the upper bound of the delay derivative must less than one is overcome. Numerical example is provided to show the effectivness of the proposed theoretical results.The passive analysis and control for stochastic interval systems with interval time-varying delay are studied. In virtue of the approach of partitioning the delay into two segments of equal length and constructing appropriate Lyapunov-Krasovskii functional in each segment of the delay interval, together with free weighting matrix and new integral equality, delay-dependent stochastic passive criteria are proposed and the passive controller is designed. The results are formulated in terms of LMIs and the passive controller can be obtained by solving LMIs. Numerical examples are given to demonstrate the effectiveness of the method.Finally, the concluding remarks are summarized, and the future works which may be further investigated are pointed out.