Research On The Stability Of Neutral Dynamical Systems

Addressed in this dissertation is the key dynamics of neutral systems and switchedneutral systems. Several relevant problems attracting more and more attention in this fieldare discussed in detail, and a series of well-established, systematical, and important re-sults is obtained.The backgrounds and research status of neutral systems and switched neutral sys-tems are introduced. It also provides the readers with some preliminaries and importantdefinitions and lemmas that are frequently used in the remaining chapters.The robust stability for uncertain linear neutral systems with discrete and distributeddelays(the single time delay and multiple time delay are included) is studied. The uncer-tainties under consideration are norm bounded, and possibly time varying. Some noveldelay-dependent stability criteria are derived and formulated in the form of linear matrixinequalities (LMIs) by a new class of Lyapunov-Krasovskii functionals which is con-structed based on the descriptor model of the system and the method of decomposition.The new criteria are less conservative than the existing ones. The examples are suppliedto illustrate the effectiveness of the results presented in this chapter.The asymptotical stability of neutral systems with nonlinear perturbations is studied.Some novel delay-dependent asymptotical stability criteria are formulated in terms of lin-ear matrix inequalities (LMIs). The resulting delay-dependent stability criteria are lessconservative than the previous ones owing to the introduction of free-weighting matricesand the Schur's lemma, based on a class of novel augment Lyapunov functionals.The delay-dependent bound input bound output(BIBO) stabilization of neutral sys-tems with multiple delays is investigated. Using the method of the descriptor modeltransformation, introducing the free-weighting matrices in the new class of Lyapunov-Krasoviskii functionals, and combining with the matrix analysis technique, the controllerwhich make the systems (BIBO) stable is designed.The stability analysis for the switched neutral systems is considered. First, wepresent new classes of piecewise Lyapunov functionals and multiple Lyapunov function-als, based on which, two new switching rules are introduced to stabilize the neutral sys-tems. One switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. The other is based on the determination of average dwell timecomputed from a new class of linear matrix inequalities (LMIs). The state-dependentswitching rule is less conservative than the existing results. Similarly, we also analyze thestability of switched neutral systems with nonlinear perturbations. Second, in differentcase, using singular Lyapunov functional and multiple Lyapunov functional respectively,the stabilization for linear uncertain neutral systems with delay in switched control in-put is investigated, and the controller is designed. Third, Based on multiple Lyapunovfunctional approach and dwell-time technique, the stability of the switched neutral sys-tems which both contain the stable subsystems and unstable subsystems is considered.The switching rule which make the switched systems exponential stable is designed. It isshown that by suitably controlling the switching between the stable and unstable modes,the robust stabilization of the switched uncertain neutral systems can be achieved.The problem of delay-dependent bounded input bounded output (BIBO) stability fora class of switched uncertain neutral systems is studied. The uncertainty is assumed tobe of structured linear fractional from which includes the norm bounded uncertainty as aspecial case. First, by introducing the general variation-of-constants formula of neutralsystems with perturbation, the BIBO stability property of general linear switched neutralsystems with perturbation is established. Next, based on the dwell time approach, andcombined with the introduced free-weighting matrices, the BIBO stability criteria are ob-tained in terms of linear matrix inequalities(LMIs). Finally, the simulation examples aregiven to demonstrate the effectiveness and the potential of the proposed techniques in thischapter.We summarize the main results obtained in this dissertation, and point out the futureworks that have been the author's concerns.