| This thesis investigates D-stability and spectrum assignment problem ofstochastic It(?) systems, and robust stability of stochastic systems withMarkovian jumps via a linear matrix inequality approach. Then we design theN2/H∞controller and static output feedback controller, respectively.Firstly, we investigate the problem of H2/H∞design with stochasticallyD-stability constraints. We discussed the D-stability of stochastic systemsand made progress to the regional D-stability Theorem. Then we considered theproblem of H2/H∞state-feedback control with regional stability constraintsfor a class of stochastic systems.Secondly, we have investigated the problem of state-feedback H2/H∞designtogether With placing the spectrum in a vertical strip, for which a sufficientcondition was presented in terms of convex optimization method.Thirdly, we dealt with the class of stochastic hybrid systems. LMI resultson asymptotically mean-square stability and stabilizability and their robustnessare developed, i static output feedback controller is designed to make theclosed-loop stochastic systems with Markovian jumps robustly asymptoticallymean-square stable. The controller gains are determined by solving a set ofcoupled LMIs either for the nominal or the uncertain systems. A numerical examplehas been illustrated to show the use of our results.
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