Stability and stabilization of stochastic systems with multiplicative noise

In this paper, stability and stabilization of linear stochastic time-invariant systems are studied based on spectrum technique. Firstly, the relationship among mean square exponential stability, asymptotical mean square stability, second-order moment exponential stability and the spectral location of the systems is revealed with the help of a spectrum operator L _A,C . Then, we focus on almost sure exponential stability and stochastic stabilization. A criterion on almost sure exponential stability based on spectrum technique is obtained. Sufficient conditions for mean square exponentially stability and asymptotic mean square stability are given via linear matrix inequality approach and some numerical examples to illustrate the effectiveness of our results are presented.