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Stability Analysis And Control Of Linear Systemswith Time-Varying Delays

Posted on:2016-10-07Degree:MasterType:Thesis
Country:ChinaCandidate:H SuFull Text:PDF
GTID:2308330461454710Subject:Operational Research and Cybernetics
Abstract/Summary:PDF Full Text Request
Time delay has been widely applied in various practical systems and real life, Therefore, it is important to analysis the stability of delayed continuous system. However, seldom have the existing methods contributed on the linear systems with two additive time-varying delays, state and input time-varying delays and uncertain systems with multiple time-varying delays so far. So it is very crucial to study the problem with the above system, which has the widely prospects and the very high practical vale and significance of important theory.In this paper, we study the stability and control problem of linear systems with time-varying, using the second method of Lyapunov and the linear matrix inequality method, combined with the integral inequality method, we can obtain the stability criteria of system that have been less conservative. The main contents are followed.(1) Firstly, we design a new inequality lemma based on the Park inequality and the reciprocally convex combination inequality, consider to the linear system of time delay, constructing a suitable Lyapunov function and applying the new lemma and LMI method, a less conservative stability conditions are obtained. Then on the basis of this we discussed the control problem for linear time delay systems, respectively with only state delay, input delay and also input and state time delay condition we give the controller design method.(2) We improve the inequality based on lemma 3.1, consider to the two additive delay linear system, by constructing a suitable Lyapunov function and applying the new lemma and LMI method, a less conservative stability conditions are obtained.(3) The fifth chapter discusses problems of linear system with multiple time delays and uncertain time delay problem of parametric terms. At first, we improved the Lyapunov–Krasovskii function and the inequality criteria for linear systems with multiple time-varying delays and obtained a sufficient condition theorem, and then on this basis, we obtain a new stabilization criteria with multiple time delays and uncertain terms.Numerical examples to show the results are less conservative and effective in each chapter. In the last part, we summary of the full text and give the future directions for our papers. Keywords: two additive delay, state and input delay, stability...
Keywords/Search Tags:two additive delay, state and input delay, stability analysis, Linear Matrix Inequality(LMI), state feedback controller
PDF Full Text Request
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