Stability Analysis And Filter Design Of Time-Delay Systems

In this thesis, the problems of stability analysis and H∞filtering are discussed for several classed of linear/nonlinear time-delay systems, including linear systems, Markov jump systems, nonlinear systems represented by T-S fuzzy models and net-work control systems. Recently, filter design for time-delay systems is a research subject of great practical and theoretical significance, which has received consider-able attention, and much significant work has been carried out. In this thesis, some new approaches will be developed to solve the stability analysis and H∞filtering design problems for several kinds of time-delay systems. The merit of the proposed approaches lie in their less design conservatism, which is realized by utilizing some more advance techniques such as linear matrix inequality (LMI) approach, piecewise analysis method, convexity property of the matrix inequality and more powerful re-laxation techniques. More specifically, the frame and description of this thesis are given as follows:●In Chapter 1, the introduction of the thesis are given, including the background and motivation, the outline and contribution, and the research contents to be introduced in each individual chapters.●In Chapter 2, the H∞filter design problems are discussed for a class of continue-time systems with time-varying delay and stochastic delay. In Section 2.2, Based on a piecewise analysis method and using the convexity property of the matrix inequality, new criteria are derived for H∞filtering, which can lead to much less conservative analysis results. A numerical example is given to demon-strate the effectiveness and the merit of the proposed method. In Section 2.3, we design an H∞filter for a class of linear time delay systems with random delay. The delay considered here is assumed to be satisfying a certain stochas-tic characteristic. Corresponding to the probability of the delay taking value in different intervals, a stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the information of the probability distribution. Then, new criteria are derived for the filtering-error systems, which can lead to much leas conservative analysis results. It should be noted that the solvability of the obtained criteria depend on not only the size of the delay, but also on the probability distribution of it. A numerical example is given to demonstrate the effectiveness and the merit of the proposed method.In Chapter 3, the H∞filter design problems are addressed for a class of Markov jump systems (MJSs) with time-varying delay. In Section 3.2, we propose an H∞filter design for MJSs with time delay. Firstly, by exploiting the delay partitioning-based Lyapunov function, new criteria are derived for the H∞per-formance analysis of the filtering-error systems, which can lead to much les conservative analysis results. Secondly, based on the obtained conditions, the filter gain can be obtained in terms of LMIs. Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed method. In Section 3.3, we propose a class of H∞filter design for MJSs with time-varying delays. Firstly, by exploiting a new Lyapunov function and using the convexity property of the matrix inequality, new criteria are derived for the H∞performance analysis of the filtering-error systems, which can lead to much less conservative analysis results. Secondly, based on the obtained conditions, the gain of filter can be obtained in terms of LMIs. Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed method.In Chapter 4, we deal with the stabilization, reliable control and H∞filter design problems for a class of nonlinear described by T-S fuzzy model. In Sec-tion 4.2, we design a memory controller for T-S fuzzy discrete-time systems with random input delay. A novel state space model with the compensator for the effects of the stochastic input delays is derived by introducing stochas-tic variables satisfying Bernoulli random binary distribution and using state augmentation method. Based on the new built model, memory controller is designed and sufficient conditions for the stochastic mean square stable of T-S fuzzy discrete-time systems are obtained by using Lyapunov functional method. Finally, a numerical example is given to show the effectiveness of the proposed method. In Section 4.3, a reliable control problem for T-S fuzzy discrete system with stochastic sensors and actuators faults is investigated. The faults of each sensor or actuator occur randomly and its failure rates are governed by two sets of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of every sensor or actuator, a new fault model is proposed. Based on the new fault model, reliable controller is de-signed and sufficient conditions for the exponentially mean square stability of T-S fuzzy systems are derived by using Lyapunov functional method and LMIs technique. Finally, a numerical example is given to show the effectiveness of the proposed method. In Section 4.4, H∞filter design for nonlinear systems with time-delay via T-S fuzzy model approach is investigated based on a piecewise analysis method.Based on a piecewise analysis method, the variation interval of the time delay is firstly divided into several subintervals, then the convexity property of the matrix inequality and the free weighting matrix method are fully used in this paper. Some novel delay-dependent H∞filtering criteria are expressed as a set of LMIs, which can lead to much less conservative analysis results. Finally, a numerical example is given to illustrate that the results in this paper are more effective and less conservative than some existing ones.●In Chapter 5, the reliable H∞filtering are considered for a class of network control systems (NCSs) with randomly varying sensor delay and stochastic sensor-failure. In Section 5.2, we design an H∞filter for NCSs with randomly varying sensor delay. A stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established. By using LMIs technique, sufficient conditions are derived for ensuring the mean-square stochastic stability of the filtering error systems. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach. In Section 5.3, we study a class of network control systems with stochastic sensor-failure, a more general NCS model is established with considering non-ideal Quality of Service(QoS). By using the convexity property of the matrix inequality and LMIs technique, new criteria for the stochastic mean square stable of NCSs are derived for the target systems. It should be noted that the solvability of the obtained criteria depend on not only the sensor induced delay, but also on the probability sensor-failure. A numerical example is given to demonstrate the effectiveness of the proposed method.●In Chapter 6, the main contents of this thesis are summarized and a few po-tential topics for further research are pointed out.