Dynamical Behaviors About Several Kinds Of Stochastic Differential Systems

Stochastic differential system has been one of the most important discussion topicsfor the scholar. Recently, both analysis and synthesis problem for stochastic systems havebeen extensively studied and a great number of important results have been reported, suchas stability analysis for stochastic systems, robust control and filter design problems andso on. In this dissertation, the dynamical behavior about two kinds of stochastic systemsis discussed, one is stability and dissipativity analysis for discrete-time stochastic neuralnetworks with time-varying delays; other one is robust fault detection and passification ofMarkovian jump systems.Firstly, the problem of exponential stability for a class of uncertain discrete-timestochastic neural network with time-varying delays is investigated. By constructing asuitable Lyapunov-Krasovskii functional, combining the stochastic stability theory andthe free-weighting matrix method, some sufficient conditions are established to ensure thestochastic neural networks are globally exponential stability in the mean square, which areproved to be less conservative than previous results. Finally, some numerical examplesare given to demonstrate the effectiveness of the proposed results. To the best of ourknowledge, few authors have considered the problem on the dissipativity of discrete-timestochastic neural networks with time-varying delays and this problem also has much moreimprovement space. Motivated by the above discussions, the global exponential dissipa-tivity in mean for uncertain stochastic discrete-time neural networks is studied. By com-bining with the convex combination theory, a new sufficient condition for checking theglobal dissipativity of the addressed stochastic discrete-time neural networks is obtained.Secondly, with the rising demand for higher safety and reliability standards in themodern industries, the robust fault detection filter design problems for uncertain nonlin-ear Markovian jump systems is studied. By using a observer-based fault detection filter asresidual generator, the robust fault detection filter design is formulated as an H∞-filteringproblem. Particularly, two different Markov processes are considered for modeling therandomness of system matrix and the state delay, which is not only theoretically inter-esting and challenging, but also very important in practical applications. By using a newconvex polyhedron technique, it will reflect the superiority of our conclusions. Finally, the problem of delay-dependent passivity analysis and passification of un-certain Markovian jump systems with partially known transition rates is investigated. Thepassivity and passification problem has played an efficient role in both electrical networkand nonlinear control systems, and provides a nice tool for analyzing the stability of sys-tems, this is a reason for our research. By combining with Jensen inequality, a desiredpassification controller is designed, which guarantees that the closed-loop system is pas-sive.