Robust Control For Time Delay Systems With Uncertainty And Its Application To Communication Networks

Controlling time delay systems with uncertainty is of significant values in control theory and application. This dissertation derives robust controller for continuous and/or discrete time systems with time-varying delays. We apply industrial communication network to light disposition systems, and design robust controller for the networked control systems and ATM communication networks. The main results and contributions of this dissertation are as follows:(1) For a class of linear systems with uncertain parameters and unknown time varying delay in control input, a robust memoryless controller, guaranteeing asymptotic stabilization, is derived in terms of a linear matrix inequality (LMI) depending on the size of time delay and on the size of delay derivative. When the states of the time delay systems are not all measurable, an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are also dependent on the size of time delay and on the size of delay derivative.(2) A new robust H∞ control method is presented for the discrete systems with parameter uncertainty and time-delayed uncertainty. When a matrix inequality is satisfied, based on the modified Lyapunov function, the system without unknown disturbance can be quadratically stabilized under static state feedback control. Furthermore, when another matrix inequality is satisfied, the system with unknown disturbance can be quadratically stabilized with a disturbance attenuation γ under static state feedback control by an innovative passive control method. If a linear matrix inequality (LMI) is solvable, the gains of the memoryless feedback controller can be obtained from the solution of the LMI, and the state of system is asymptotically tracking to the designed reference signal.(3) When subsystems are connected by network, there exist time delays and asynchronism. We propose a new robust H∞ control method based on the Algorithm Riccati Inequality (ARI) and/or Linear Matrix Inequality (LMI) approach for the robust control of the systems. The uncertainty of time delays is converted to the uncertainty of the parameter matrix, and the states are transformed to the augmented states to eliminate the effect of the asynchronism. When there is no disturbance, the closed-loop system can be quadratically stabilized by the static state feedback. When the system is affected by unknown disturbance, the closed-loop system can be quadratically stabilized within a disturbance attenuation γ. For the high-speed communication networks with one bottleneck node and multiple sources, the exponential tracking performance of each source rate to the relevant bandwidth allocation fairness, as well as the queue length to the reference, shows the effective utilization of the networks subject to low loss rates. When the available bandwidth is constant, based on LMI and delay time-derivative dependent control methods, a robust controller is designed to achieve exponential tracking stability. The controller needn't tune the parameters, and computing complex is comparatively low. When the available bandwidth, i.e., available throughput capacity, of bottleneck is time varying and unknown, a robust controller is designed to achieve small tracking error guaranteeing high performance. Upon the results of four LMIs, which can be solved simultaneously, we can get the gain of the controller.