Stability And Controllability Of Hybird Stochastic Differential Delay Equations

The stochastic control theorey is one of the most important issues in the study of stochastic differential delay equations. It has been applied widely in economics,biology, ecology, engineering, etc. So the study of stochastic control theory has high value of utility.In this paper, the conditions for stability of linear hybird stochastic differential delay equations with state feedback controller are studied. Firstly, a class of criteria for designing a linear state feedback controller in diffusion terms to stabilize a linear hybird stochastic differential delay equations almost surely is given by using Lyapunov methods and Linear Matrix Inequalities techniques, which expressed in terms of linear matrix inequalities. Then a class of criteria for designing a linear state feedback controller both in drift terms and diffusion terms is also given using the same method. At last we discuss one example to illustrate our theory.Finally, we investigate the almost surely asymptotic stability and controllability for the nonlinear hybird stochastic differential delay equations in the paper. A class of criteria for designing a state feedback controller in drift terms to stabilize a nonlinear hybird stochastic differential delay equations almost surely is given in the same way.And then a class of criteria for designing a linear state feedback controller both in drift terms and diffusion terms is also given using the same method, which expressed in terms of linear matrix inequalities.