Reliable Control And Filtering For Some Classes Of Stochastic Nonlinear Time-delay Systems

With the development of science and technology, control systems become more and more complicated. It is inevitable that actuator failures or sensor failures may exist in the systems, which will affect the stability and other performance of the systems. Therefore, the demands for reliability, safety and efficiency of the systems are higher and higher. This dissertation is concerned with the problems of stability analysis, reliable control and reliable filtering for some classes of stochastic nonlinear time-delay systems in the presence of actuator failures or sensor failures. The main contributions are as follows.The reliable control problem against actuator failures for a class of stochastic nonlin-ear time-delay systems with multiplicative noises is investigated. First of all, the stochastic nonlinearities are introduced as exogenous nonlinear disturbances which are described by statistical means. The time-delay term is involved in the stochastic nonlinearities, which are therefore more general than the corresponding ones in the related literature. The actuator failures are described by a variable taking values in some interval. This model is called continuous gain actuator failure model, which is more practical than the con-ventional outage case. Next, the exponentially mean-square stability conditions of the closed-loop system are obtained by using the Lyapunov-Krasovskii functional and LMI technique, which are dependent on the lower and upper bounds of the time-varying delay. Therefore, the obtained conditions are less conservative. Then, a state feedback controller is designed based on the stability analysis. The controller gain is characterized in terms of the solution to a set of LMIs.The reliable H∞output feedback control problem against actuator failures for a class of time-delay systems with randomly occurred nonlinearities (RONs) is studied. RONs are introduced to model a class of sector-like nonlinearities that occur in a probabilis-tic way according to a Bernoulli distributed white sequence with a known conditional probability. The mean-square asymptotic stability conditions of the closed-loop system with a prescribed H∞performance level are obtained by using the Lyapunov-Krasovskii functional and LMI technique. Based on the stability analysis and using the technique of linearizing change of variables, an observation-based H∞output feedback controller is designed. The obtained results are delay-dependent and less conservative.The reliable H∞filtering problem against sensor failures for a class of time-delay systems with randomly occurred nonlinearities (RONs) is considered. By using a novel Lyapunov-Krasovskii functional and delay-partitioning technique, asymptotically mean-square stability conditions of the filtering error dynamics with a prescribed H∞perfor-mance level are obtained, which are delay-dependent. An auxiliary matrix is introduced to realize the decoupling between the Lyapunov matrices and the filtering error system matrices, which can reduce the conservativeness. Based on the stability analysis, a reliable H∞filter is designed. The filter gains can be obtained by solving a set of LMIs.The reliable H∞filtering problem against sensor failures for a class of nonlinear Markovian jumping systems with time-varying delays is addressed. The transition proba-bilities of the jumping process are assumed to be partly unknown. The nonlinearities are introduced as exogenous nonlinear disturbances which are described by statistical mean-s. By using a novel Lyapunov-Krasovskii functional and delay-partitioning technique, delay-dependent sufficient conditions are obtained under which the filtering error system is asymptotically mean-square stable with an H∞performance level. An auxiliary matrix is introduced to realize the decoupling between the Lyapunov matrices and the filtering error system matrices in order to reduce the conservatism. The developed results are more general since they can be applied to Markovian jumping systems with completely known, completely unknown and partly unknown transition probabilities.Finally, the results of the dissertation are summarized and the further work are pointed out.