Robust Control Of Uncertain Time-Delay Systems

This paper studies the problem of robust control of uncertain time-dela ysystems. The development of robust control theory and linear matrixineq uality (LMI) technique is summed up at first, and then according todifferent uncertain time-dela y systems, the robust stability condition and themethod of robust controller design of these systems are studied. It is asfollows.First, the problem of absolute stability for Lurie control systems withtime-varying delays is investigated. For the Lurie systems subject to bothtime-varying delays and parametric uncertainties, sufficient conditions ofrobust stability are deduced based on Lyapunov method and Finsler's lemma.The proposed conditions are in terms of linear matrix ineq uality (LMI) whichcould be easily solved by MATLAB toolbox.Second, this paper studies the problem of robust stability and H-infinitycontrol for a class of uncertain Markovian jump linear systems with timedelays. Sufficient conditions for the existence of a robust and H-infinitycontroller are derived. By using the change of variables and Schurcomplements,the obtained conditions can be rewritten as a set of coupledlinear matrix equalities (LMIs),and the H-infinity controller can beconstructed through the numerica l solution of these LMIs．Third, the problem of the reliable guara nteed cost control based on a [0, σ] model of failure is investigated for a class interconnected uncertainsystems with time-varying delays, nonlinear perturbation, parameteruncertainties containing actuator failure. By using Lyapunov approach andlinear matrix ineq uality (LMI) techniq ue, a sufficient condition for theexistence of the reliable guara nteed cost controller is derived, which rendersthe system a guara nteed cost.