Robust H_∞ Control For Uncertain Time-Delay Systems And Its Application In Networks' Congestion Control

It is always impossible to obtain accurate mathematics model for the practical industrial processes. The model under which the controller is designed is usually different to the real plant owing to model reduction, linearity approximations and the ignoring of the dynamics difficulty for modeling, the changing of the operating environment and other unmeasurable disturbances. These differences usually can be described as the uncertainties in the model arguments. Robust control, the control design method considering such uncertainties when designing controller is a effective way to deal with the uncertain parameters. On the other hand, because of transmission process, large-lag links and complicated on-line analyzer etc, a large number of industrial processes (in metal engineering, chemical engineering systems, biomedical systems and so on) can be modeled as time-delay systems. The stability and performance are always dominated by delay phenomena, so the study of delay systems always attracts considerable attention in the control theory literature.In this paper, kinds of robust stabilization and robust H control problems forlinear uncertain time-delay systems are studied in detail. As to the frequency domain methods, the physical significations of the H performance targets, the selectionstrategy of the weighting functions, loop-shaping and standard problems of robust H control are discussed. Frequency domain design methods of robust H controlare also introduced to solve the congestion control problem of the high-speed communication networks, which based on flow rate control. On the other hand, as to the time domain methods, based on Lyapunov-Krasovskii function method, Riccati equation method, linear matrix inequality technique, along with the skills of equality and inequality transformations, the robust stabilization and robust H controlproblems are studied via state feedback for some kinds of uncertain time-delay systems, and delay-independent as well as delay-dependent results are obtained. The main contents of this paper are outlined as follows,(1) The physical significations and the correlativities of the often-used Hperformance targets are summarized, the selection strategies of the weighting functions are researched, and loop-shaping method as well as standard problems of robust H control are introduced. The frequency domain methods of robust Hcontrol are also introduced to solve the rate-based congestion control problem of thehigh-speed communication networks, and the H based controller are designed todeal with the time-delay problem of the single bottleneck node and multiple resources networks.(2) For linear systems with time-varying delays both in state and control, and subject to norm-bounded parameter uncertainties, the problems of robust stabilization and robust H control are studied and delay independent results are derived byconstructing proper Lyapunov function to deal with the time-delay, also by using Riccati equations method and inequalities transformations to deal with the uncertainties. According to the transform function of the system, frequency domain method and time domain method are combined together to analyze the robust Hcontrol problem of the uncertain time-delay system.(3) A new design approach of delay-dependent robust stabilization and robust Hx controller for a class of uncertain time-delay systems is provided. The sufficient conditions of delay-dependent robust stabilization and robust H control, which are simpler, less conservative and can be used to deal with not only small delay systems but also large delay systems, are derived based on a new state transformation and given in terms of linear matrix inequalities (LMIs).(4) For a class of uncertain time-delay systems with multiple-state delays, new delay-dependent robust stabilizability and robust H Control criteria are derivedbased on Lyapunov-Krasovskii functional method and given in terms of linear matrix inequalities (LMIs), which are proved by the numerical examples to be...