On stabilization of linear systems with stochastic disturbances and input saturation

It is well-known that for linear systems internal asymptotic stability implies external stability in the sense that when the external input is in L_p then also the state will be in L_p. However, for the control of linear systems with saturation where the controlled system is nonlinear this implication is no longer directly applicable. Several people have studied the effect of external inputs in L_p either directly or in the context of ISS as introduced by Sontag. In this paper we study the effect of external stochastic disturbances on linear systems with input saturation and we establish that when we can achieve internal global asymptotic stability then we can also achieve a bounded variance for the state.