A Study On Robust Control For Uncertain Time-delay Systems

People always want to obtain the exact mathematics models for the practical industrial process control problems. However, the model under which the controller is designed is usually different from the real plant because there are model reduction, linear approximations and the ignoring of the dynamics difficulty for modeling. Usually, these differences can be described as the uncertainties in the model arguments and the uncertainties are measurable and can be restricted in some range. Robust control theory is an effective way to deal with the control problems with the uncertain systems. On the other hand, large-lag links, transmission process and complicated on-line analyzer etc, are common in a number of industrial processes , which can cause delay in the systems. Such delays will be a main cause of bad performance or even instability for control systems. So, the research on the time delay systems attracts considerable attention in the control theory literature all alone.Based on Lyapunov stability theory, Razumikhin stability theory and convex set theory, also by using linear matrix inequality, matrix analyzing methods and convex programming methods, we studied some kinds of robust control problem for uncertain time delay systems in details. Concerning the time delay systems with norm-bounded uncertainties or convex polyhedron uncertainties, the problems of robust stability criteria, the design methods of robust stabilizing controller and the design of controller that guarantee certain robust performance by state feedback or output feedback are investigated. The results can be classified as delay-independent and delay-dependent. The main contents of this paper are outlined as follows,1 For time delay systems with norm-bounded uncertainties, a sufficient and necessary delay independent robust quadratically stabilizable condition, the corresponding robust stabilizing controller designingmethod by state feedback, a sufficient delay-dependent robust stabilizable condition and state feedback controller designing method are given in terms of linear matrix inequalities. A numerical simulation example is given to illustrate the obtained results.2, For time-delay systems with uncertainties, an output feedback robust stabilizable condition is introduced and robust Hx control problems are studied. We reviewed the delay-independent robust stabilizing controller design method and the robust Hx controller designing method by output feedback is obtained.3, The optimal guaranteed control problem for a class of linear time delay systems with norm-bounded uncertain parameters is considered. The delay- independent optimal controller designing method by output feedback is achieved.4, The optimal guaranteed control problem for a class of linear tune-delay systems with convex polyhedron uncertain parameters is considered. A state feedback controller designing method is given in terms of linear matrix inequalities.5. For systems with state and control delays and norm-bounded uncertainties, we investigate the reliable Ha control problems of such systems and the reliable Hx controller by state feedback is obtained.6, The problem of robust stability analysis for a class of uncertain systems with nonlinear perturbations is studied. Based on the positive definite solutions of a Linear Matrix Inequality, a robust stability criteria is derived. A numerical example is studied to illustrate the obtained results.The conclusion and perspectives are given in the end of the paper.