Stability and stabilization of stochastic systems by feedback control

In this paper, stability and stabilization of linear stochastic time-invariant systems are studied based on spectrum technique. First, some definitions of stability are given. With the help of a spectrum operator LA,C, the relationship among mean square exponential stability, asymptotical mean square stability, 2th moment exponential stability, the spectral location of the systems is revealed. Second, a criterion on almost surely exponential stability based on spectrum technique is obtained. Finally, we give sufficient conditions for mean square exponentially stability or asymptotic mean square stability via linear matrix inequality (LMI) approach.