On The Robust Absolutely Stability Of A Class Of Uncertain Time-Delay Systems

There often exist time-delay phenomena in most practical industrial processes control systems, especially in the case of large size of industrial device. For example, petroleum chemical engineering systems and metallurgy systems can be modeled as time-delay systems for their content lag and transmission delay. And it isn't a rare phenomenon for several ten minutes of delay. In addition to these, some large-lag links and complicated on-line analyzer etc can also result in time-delay. Systems stability and performance are always influenced badly by lag. So the study of delay systems always attracts considerable attention in the control theory.On the other hand, Because of the changing of the physics and chemistry for outside environment and other unmeasurable disturbances, the model under which the controller is designed is usually different to the real plant owing to model reduction. So it is always impossible to obtain accurate mathematics model for the practical controlled plant. And the difference of which some measure can be given usually can be described as the uncertainties in the model arguments. Robust control considering suchuncertainties when analyzing stability and designing controller is a effective way to deal with the uncertain parameters.In this paper, state-space method is adopted to study a class of ubiquitous nonlinear systems, namely Lurie systems. Based on the existed results, this paper considers two kinds of simultaneous cases, that is time-delay and uncertainties, to get the solution of uncertain Lurie time-delay system by means of Lyapunov stability theory and LMI toolbox. At the same time, the robust absolute stability conditions and the design method of robust controllers of Lurie direct-type and indirect-type delay systems are given.The design methods of robust stabilizing controller and guaranteeing certain robust performance controller for Lurie-type delay systems with norm-bounded uncertainties are studied by delay independent method and delay dependent method. In this paper we adopt the delay dependent method for the conservativeness of delay independent method. The main contents are as follows:1. For the advantages and simplicity of LMI toolbox in resolving control problems currently, the chapter 3 of this paper introduces some basic concepts about Linear Matrix Inequalities (LMIs). Three solvers of LMI toolbox of the software Matlab is also presented. A review on the theory and application research for LMI in control systems is described in detail, mainly including robust control and robust filtering ofuncertain systems. At the same time, some nonlinear systems and time-delay systems are discussed. And then, a list of the latest results of some representative control problems via the LMI approach is introduced. Finally, an example is presented to illustrate the procedure of solving LMIs, and the associated programme is also given.2. The problems of robust stability for a class of Lurie direct or indirect systems with time-delay and norm-bounded uncertainties are discussed using delay dependent method. Method of linear matrix inequality is adopted to resolve the problems. Comparing with the other sufficient conditions, the maximum delay obtained in this paper is less conservative.