Robust Analysis And Control For It(?) Stochastic Differential Systems With Time Delay And Markovian Switching

The hybrid systems driven by continuous-time Markov chains have been used to model many practical systems, where they may experience abrupt changes in their structure and parameters, such as component failures or repairs, changing subsystem interconnections, and abrupt environmental disturbances. Moreover, it has been well recognized that time-delay and uncertainties cannot be avoided in practice and often results in instability and poor performance. Besides, it is necessary to take the envir -onmental noise into account. Therefore, robust analysis and control for Ito stochastic differential delay systems with Markovian switching are very important in control theory and its applications. This dissertation deals systematically with the stability analysis, robust analysis, robust control and design filtering of concern systems. The contributions can be concluded as follows:[1]The stochastic controllability problem for a class of Ito stochastic differential systems with Markovian jump parameters switching is addressed and studied. By us -ing an approach to the Martingale Inequality, Sufficient conditions are established to guarantee the stochastic controllability, which are given in terms of the solutions to a set of coupled Bernoulli equations.[2]The robust exponential stability of time-varying delay uncertain Ito stochastic differential systems with Markovian jump parameters switching is investigated. Based on the stochastic stability theory, some sufficient criteria are obtained in terms of LMIs and they can be conveniently verified that the sufficient conditions should be proved to be very useful in applications.[3]The robust stabilization for a class of uncertain Ito stochastic differential systems with time-vary delay and Markovian switching is considered. Our attention is focused on the design of a robust state-feedback controller such as for all admissible uncertainties, the closed-loop system is stochastically exponentially stable independ -ent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set linear matrix inequalities.[4]The robust Ha analysis and control problems for a class of uncertain ltdstochastic differential systems with time-vary delay and Markovian switching are investigated. A delay-independent bounded real lemma for concern systems is presented in terms of LMIs. Based on bounded real lemma obtained, delay-indep-endent conditions for the existence of robust Hx controller are obtained in terms ofthe solution of a set of LMIs.[5]The robust Hx filtering problem for a class of uncertain ltd stochasticdifferential systems with time-vary delay and Markovian switching is addressed and studied. The purpose of this problem is design a full filter such as the dynamics of the estimation error is guaranteed to be stochastically exponentially stable. Both filter analysis and filter synthesis problems are considered. Sufficient conditions are proposed for the existence of desired exponential filter.[6]The exponential stability and Hx analysis problems for a class of nonlinear ltdstochastic functional differential systems with Markovian switching are studied. A Razumikhin-type theorem on the exponential stability in the mean square for concern systems. By using the Razumikhin theorem and generalized Ito formula, Sufficient conditions for the time-delay stochastic systems with Markovian switching to beinternally stable are established. The Hx analysis problem is studied in order toquantify the disturbance rejection attenuation level of the nonlinear stochastic time-delay system with Markovian switching. Some easy-to-test criteria are given so as to determine whether the nonlinear stochastic time-delay jumping system is internallystable and whether it achieves certain Hx performance index.