Generalized Time-varying Delay Lpv Systems Of Time-delay Dependent Robust H_ Up Filter

This thesis is concerned with the problems of admissibility analysis, boundedreal lemma, robust H∞fltering for singular linear parameter varying (LPV) systemswith time-varying delays as well as the problems of D-stability and D-stabilizationfor discrete singular time-delay LPV system. Additionally, the stability analysis oflinear systems with interval time-varying delay and nonlinear perturbations is alsoconsidered in this paper.Firstly, a delay-dependent admissibility criterion described by linear matrixinequalities (LMIs) is obtained based on the construction of a new parameter-dependent Lyapunov function. On the other hand, for the singular time-delaysystems, a new less conservative delay-dependent stability criterion is obtained forsingular time-varying delay system based on a so-called piecewise analysis method.Secondly, a delay-dependent bounded real lemma is presented in terms of LMIsto ensure a class of singular time-delay LPV systems to be admissible and satisfy aprescribed H∞performance level. On the other hand, based on a so-called piecewiseanalysis method, a new less conservative delay-range-dependent bounded real lemmais presented.Thirdly, based on the obtained delay-range-dependent bounded real lemma, asufcient condition is presented to ensure the fltering error singular time-delay sys-tems to be admissible and satisfy a prescribed H∞performance level. Furthermore,a sufcient condition for the existence of such a flter is proposed in terms of LMIs.Fourthly, the problems of D-stability and D-stabilization is concerned for de-scriptor discrete time-delay LPV systems. By constructing parameter-dependentLyapunov functions, sufcient conditions are presented in terms of LMIs such thatall the poles of a corresponding system lie in a specifed circular region.Finally, this paper focuses on the stability analysis of a class of linear systemswith interval time-varying delay and nonlinear perturbations. New stability criteria for the class of systems are obtained by combining Jensen inequality and delaydividing approach. It is numerically investigated that the proposed stability criteriaproposed are less conservative than those in literature.The efectiveness of these methods proposed in this thesis are demonstrated bynumerical examples and their simulation results.