Robust Stability Of Uncertain Delay Systems

At present the robust stability analysis of systems with uncertain time-delay is focused on automatic control field. Many factors, such as changing of systems environment, the age of components, and some physical param-eters and so on, can bring about changes of the systems behaviors. Those will cause uncertainty and time-delay of the system models. The existence of uncertainty and time-delay makes the system analysis and synthesis become more complex and more difficult. At the same time, it is also the source of the systems instability and systems performance deterioration. Uncer-tainty, time-delay, linear, nonlinear, disturbances and adaptive tracking are considered from the perspective of theoretical analysis. Quadratic stabiliza-tion, Lyapunov stabilization, linear matrix inequalities and other important theories and methods are used in this paper. The paper studys the synthe-sis problems of the systems state feedback quadratic stabilization controller, stability controller constrained under the H∞bounded normγ, robust H∞guaranteed cost controller, adaptive output feedback controller and adaptive tracking controller, respectively. A relatively unified processing framework is proposed. The results show that the integrated problems of various systems stabilizing controller can be transformed into the feasibility of solutions of the corresponding Riccati equations (inequalities) or linear matrix inequali-ties under the certain conditions, however, the solution of Riccati equations (inequalities) and linear matrix inequalities have the sophisticated algorithms. So the research results are operable which establish the foundation for further study robust control problem of uncertain time-delay systems.