Research On Several Problems Of Time-Delay Systems

Time delays are often encountered in various practical systems. It has been shown that the existence of delays in a dynamic system may result in instability, oscillations or poor performances. Therefore, the stability analysis and the synthesis of controllers for time-delay systems have received considerable attentions over the decades.Based on the basic concepts and methods of control theory, with the help of LMI tools, through constructing proper Lyapunov-Krasovskii functional and using various derivation methods, several issues of time-delay systems are investigated in this dissertation. The major contributions of this thesis are as follows:1. The robust stability of uncertain neutral systems with mixed delays is studied. Firstly, novel Lyapunov-Krasovskii functional is constructed and its positive definiteness is proved by using integral inequality, which relaxes the constraint on some parameters of Lyapunov-Krasovskii functional. Then, by introducing slack matrices, the stability criteria are obtained in terms of LMIs, which is dependent on sizes of neutral delay and discrete delay. Theory analysis and numerical examples are given to demonstrate that the obtained results are less conservative than some existing stability criteria. Furthermore, the relationship between neutral- and discrete delay is also illustrated.2. The robust stability of uncertain neutral systems with time-varying delay is investigated. Through constructing proper Lyapunov-Krasovskii functional, using slack matrices and the convex combination condition, the stability criteria, which are dependent on the sizes of neutral delay, discrete delay and its derivative, are derived in terms of LMIs. The significant improvement on the conservativeness of the delay bound over some reported results are illustrated by theory analysis and numerical examples, and the relationships of neutral delay, discrete delay and its derivative are also presented.3. The dynamical output feedback stabilization for retarded time-delay systems is considered. A proper transformation of the closed-loop system by introducing free matrices is used and the correspondent Lyapunov-Krasovskii functional is constructed, by which the delay-dependent stability is derived. Then, the parameterization of controller is used to es- tablish the design condition in terms of LMI with respect to all parameters of controller and Lyapunov-Krasovskii functional. The desired controller is also explicitly formulated.4. The issue of stabilization for the linear neutral systems with mixed delays is concerned. Based on the model transformation of neutral type, the Lyapunov-Krasovskii functional method is employed to establish the stability criterion, which is dependent both on discrete delay and distributed delay. Then, through the controller parameterization, the desired parameters are determined under the design condition in terms of LMI, and the desired controller is also explicitly formulated. Since the considered system is a more general case, the design of controllers for some time-delay system, such as retarded time-delay system, neutral system without distributed delay, can be seen as a special case of this result.5. The fault-tolerant control for uncertain linear time-delay systems is considered. Attention is focused on the design of the dynamical output feedback controller, which maintain the asymptotically stability of closed-loop systems with sensor failures. Based on a general sensor model of failure and a less conservative stability condition, nonlinear transformation and cone-complementary linearization iterative algorithm are used, and the desired controller is obtained.6. The exponential stability in mean square for uncertain stochastic systems with time delay is discussed. The uncertainties under consideration are norm-bounded uncertainties and nonlinear uncertainties. Based on It(o|^) calculus rules and the properties of the Brown motion, through constructing proper Lyapunov-Krasovskii functional, introducing additional parameter of Lyapunov-Krasovskii functional and using slack matrices, the novel delay-dependent stability criteria are obtained in terms of LMIs. The significant improvement on the conservativeness of the delay bound over some reported results are illustrated by theory analysis and numerical examples.