A Study On Robust Stabilization For Linear Uncertain Time-Delay Systems

Time delay is a common phenomenon in industries. Many practical processes include time delays in their dynamic equations, such as biology, chemistry, economy, mechanism, physics, physiology, population and engineering etc. In addition, because of the executing time of actuator and sensor and the communication time of network, there are also time delays in the closed-loop systems, such as network control system and teleoperation system etc. At the same time, the characteristic equations of the controlled systems with time delays are transcendental equations and belong to infinite dimensional systems, so it is difficult to study the time delay systems in mathematics theory and also difficult to obtain good performance for the time delay systems using the controller designed by classical control theory. So study for the time delay systems has high theoretical and practical significance. On the other hand, it is hard to obtain the exact model of the controlled plant in practical systems, and sometimes we have to simplify the model for its complexity even if we get the exact model of the controlled plant. Besides the imprecise model, the character of the controlled plant also changes when the work condition and environment change or the gains of the system components change by aging, so it has errors with the standard characteristic of the plant and the uncertainties are occurred.Because time delays and uncertainties exist widely and both of them may cause instability and performance deterioration if not dealt with properly, it is necessary and significant to study the control for the uncertain time delay systems. In this paper, based on the Lyapunov stability theory and linear matrix inequalities (LMIs), we mainly study the problem of robust stabilization via state feedback, observer-based state feedback and output feedback for the uncertain systems with time delays,...