Research On Stability, Decentralized Control And Filtering For Large-Scale Systems With Time Delays

Due to the rapid development of industrial and agricultural production, as well as technology, there are many systems with increasingly large scale and complex structure come forth in every field of modern society, such as industry, ariculture, energy, traffic, irrigation, economy management, life science and IT technology. Generally, these systems can be treated as large-scale systems and studied consequently. On the other hand, time delay exists widely and is a main source of performance degradation even instability of systems. For large-scale systems, since there always exists large or small time delay due to information transmission among subsystems, the effect of time delay has to be considered in the analysis and design of large-scale systems. Therefore, research on the related questions of time-delay large-scale systems is of great theoretical and practical significance.In order to accelerate the development of large-scale systems to some extent and provide solutions for practical engineering problems, this dissertation focuses on studying the problem of stability, decentralized control and filtering design for time-delay large-scale systems by systematically combining many mothods and techniques, such as Lyapunov-Krasovskii (L-K) functional method, decentralized control, ruobust control, adaptive control, reliable control, fuzzy control and linear matrix inequality (LMI) technique. The main work of this dissertation is as follows:1. Based on L-K functional method and matrix norm theory, the problem of robust stability for a class of discrete-time large-scale systems with delays is investigated. The systems under consideration not only has time-varying delays but also has uncertain nonlinear interconnections. Delay-independent robust stability criterion are given as a family of Lyapunov equations and algebra inequalities, which not only has low conservativenees but also can be easily calculated.2. The problems of decentralized stabilization and tracking are considered for uncertain affine nonlinear time-delay large-scale systems, strict feedback nonlinear time-delay large-scale systems and uncertain nonaffine nonlinear time-delay large-scale systems, respectively. By choosing appropriate L-K functionals and using fuzzy approximation technique, the systems’uncertain nonlinear terms with time delays are compensated and several decentralized adaptive fuzzy controllers are proposed. Since the use of intelligent control scheme, no rigorous assumptions are imposed on the considered systems for the control design which renders the designed controllers extensive applications. Through simulations, the effectiveness of all the proposed algorithms is verified.3. The problem of decentralized model reference control is considered for a class of continuous-time large-scale systems with parameter uncertainties, time-varying delays and disturbance with unknown bound. A decentralized adaptive model reference controller is proposed by using L-K functional method, LMI technique and adaptive control approach. The rigorous matching conditions in present model refernce control are removed in our control design, even parameters of the reference model are not needed if dimensions between the considered system and reference model are compatible and the reference signals are bounded. On this basis, the problem of model reference decentralized H∞control is also considered. In order to avoid the problem of persistent increasing of adaptive parameters, the dead-zone adaptive algorithm is proposed. Meanwhile, the L2norm bounds of the tracking errors are given in order to improve the transient performance of the closed-loop system, two methods are provided to improve the transient performance.4. The problem of decentralized reliable guaranteed cost control is considered for a class of continuous-time large-scale systems with parameter uncertainties and nonlinear time-delay interconnections under actuator failures. Based on L-K functional method, sufficient condition for the existence of decentralized reliable guaranteed cost controller is derived firstly. In order to facilitate the control design, the sufficient condition is transformed into a set of LMIs which can be easy solved by using the LMI Toolbox of MATLAB. Since digital control has been turning into the mainstrain in modern industry, the problem of decentralized reliable H∞control is also considered for a class of discrete-time large-scale systems and the parameterized controller is given. The effectivness of both decentralized controllers are illustrated by simulations.5. The problem of decentralized H∞filtering for a class of time-delay larg-scale system is investigated. A linear filter is designed for every subsystem by using the subsystem’s output as the input of the designed filter. The local decentralized filter can be determined by solving only one LMI, which reders the proposed scheme small computation and low conservativeness. Aiming at achieving good H∞performance, the filter design is changed into a convex optimization solving problem constrained by LMI. A numerical example is also provided to demonstrate the feasibility of the proposed filter design method.