Robust control of uncertain time-delay systems

Time-delay systems are common in industries. Direct analysis and synthesis of control systems with time delays are complicated and approximation methods such as Pade approximation are usually applied. However, the issues of control system robustness with respect to model uncertainties and approximation errors have not been sufficiently addressed.; This dissertation focus on robustness of time-delay systems, especially robustness with respect to time delays, which has been discussed extensively using Lyapunov second method. We propose two methods in this dissertation to reformulate the problems into standard μ or $H\infty$ problems. The first method involves representing the systems in linear functional transformation (LFT) framework and approximating delays by rational transfer functions. The approximation errors are then treated as uncertainties. We show that all the well-known techniques of $H\infty$ control theory can be applied to this framework. Consequently, controller design becomes a routine process. We also show that the conventional Lyapunov method is a special case in our proposed framework and our proposed method offers less conservative results. In the second method, we treat uncertain delays as uncertainties with restricted phase angles and extend structured singular value to include phase information. We show that the extended small-μ theorem can be applied to analyze stability and performance of uncertain delay systems with many other type of uncertainties, such as plant model uncertainties and parametric uncertainties.; Finally, we generalize the above techniques to linear systems with feedback connected nonlinear elements. Both time invariant and time-varying nonlinearities are discussed by incorporating circle/Popov criterion with small-μ theorem.