Stability And Robust Control Of Delay It(?) Stochastic Differential Systems With Markov Jumping

The hybrid systems driven by continuous-time Markov chains have been usedto model many practical systems, where they may experience abrupt changes in theirstructure and parameters, such as component failures or repairs, changing subsysteminterconnections, and abrupt environmental disturbances. Moreover, it has been wellrecognized that time-delay and uncertainties cannot be avoided in practice and oftenresults in instability and poor performance. Besides, because the environmental noiseactually exists, it is necessary to take this element into account. Therefore, robustanalysis and control for delay It(o|^) stochastic differential systems with Markov jumpingare very important in control theory and its applications. On the other hand, sincethe delay of many practical systems is bounded and the infinite delay is very less,for the case of the small delay, the results which does not consider the length of thedelay are more conservative. This dissertation deals systematically with the delay-dependent stability analysis, robust control and design filtering of concern systems.The contributions can be concluded as follows:1. The stochastic exponential stability in the mean square and the almost-surestability of delay It(o|^) stochastic differential systems with Markov jumping are investi-gated. For the delay-independent criterion, based on"small scalar method", some suf-ficient criteria are obtained with less conservativeness by introducing more parametri-cal matrices; And some sufficient delay-dependent criteria for stochastic exponentialstability are obtained by constructing different stochastic Lyapunov functionals.2. The stochastic exponential stability in the mean square and the almost-surestability of It(o|^) stochastic differential systems of neutral type with Markov jumping areinvestigated. Based on the special structure of such systems, applying the generalizedIt(o|^) formula, the criterion for the stochastic exponential stability in the mean squareand the almost-sure stability of It(o|^) stochastic differential systems of neutral type withMarkov jumping are obtained by constructing Lyapunov functional in term of LMIs.3. The stochastic exponential stability in the mean-square sense of nonlinear It(o|^)stochastic differential systems with Markov jumping are investigated. For the case ofnon-delay, delay and neutral type, some new criteria are given based on Grown-Wall inequality and generalized It(o|^) formula, which improve the existed results.4. The robust control problem of delay It(o|^) stochastic differential systems withMarkov jumping is investigated. Based on the stability analysis, the approach of sta-bilization controller in the delay-independent and delay-dependent case is obtained.And based on the SLQ theory, the stabilization problem based on optimal SLQ con-troller is discussed. For norm-bounded uncertainty, the problem of robust H_∞analysisand the design approach of robust H_∞controller are investigated. And the problemof robust guaranteed cost control of such systems is proposed and solved.