Static output feedback H2/H∞ control with spectrum constraints for stochastic systems subject to multiplicative noises

This paper investigates the problem of static output feedback $ H_{2}/H_{\infty } $ control with spectrum constraints for linear continuous-time stochastic systems with state dependent noises. By using the spectrum technique, the notion of $ \mathbf {D}(-\beta , -\alpha ) $ stability for continuous-time stochastic systems is proposed. Subsequently, the design method of the static output feedback controller is presented by solving a set of linear matrix inequalities. Under $ \mathbf {D}(-\beta , -\alpha ) $ stability, a sufficient condition for the existence of stochastic $ H_{2}/H_{\infty } $ control is derived, which transforms the problem of $ H_{2}/H_{\infty } $ control into a convex optimization problem. Finally, a numerical example is given to show the effectiveness of the obtained results