Stability Analysis And Robust H_∞ Control For Time-delay Systems

Time delay exists in many kinds of industrial systems. Because of a large quantity of time delay systems existing and the difficulty of the analysis and control of these systems, the analysis and synthesis of time-delay systems always is a hot issue of the research in the control theory and control engineering field.Stability is a basic structural characteristic of system. Stability problem is an important subject about research on the theory of system control. In most of the cases, stability is the premise of normal work for practical systems. The H_∞control theory for systems has been investigated well in robust control theory. In the paper, stability problems and robust H_∞control for time-delay systems are mainly researched.The main contents and contributions in the paper are as follows.(1) Basing on linear matrix inequality, the sufficient condition of this system with general T-suboptimal H_∞performance is presented; furthermore, it is shown that the general bounded real lemma for descriptor discrete system is extended to the case involving system with multiple time delays in a certain way; finally, the sufficient condition of the corresponding normal system withγ-suboptimal H_∞performance is given. And the numerical example is presented to illustrate the efficiency of this result.(2) The analysis of guaranteed cost robust stability for nonlinear system with time-varying delays is investigated. Firstly, the sufficient condition of this system with the property is obtained, in terms of linear matrix inequality. Secondly, when time delay in this system becomes single and not time-varying one, the corollary deprived from the result above is much little conservative than the result in reference [30], which can be illustrated by the numerical example given.(3) The improving conditions for the solvability of the delay-depended robust H_∞control problems for uncertain state-delay systems is considered. Firstly, in the pre-knowledge, an important proposition-general integral inequality is obtained; secondly, depended on the obtained general integral inequality, an improved delay-dependent bounded real lemmas(BRLs) for these autonomous systems are proposed in terms of linear matrix inequalities(LMIs); thirdly, basing on obtained RBLs, the sufficient conditions for existence of robust H_∞controllers and the algorithms of these controllers are presented. At the same time, more general results are obtained in comparison to existing ones. By letting R=αP (for someα＞0), the obtained nonlinear matrix inequality conditions are converted to LMI ones. At last, three numerical examples show that the proposed conditions in the paper are much less conservative.