Infinite-horizon linear quadratic optimal control for discrete-time LTI systems with random input gains

In this paper we continue our study of the infinite-horizon linear quadratic (LQ) optimal control for linear time-invariant (LTI) discrete systems with random input gains. In our previous work, it is shown that the LQ optimal control problem with an internal stability requirement is solvable if and only if a mean-square stabilizing solution to the associated modified algebraic Riccati equation (MARE) exists. Moreover, the optimal controller is a linear state feedback. In this paper, we focus on investigating the conditions ensuring the existence of a mean-square stabilizing solution to the MARE. The observability and detectability as well as stabilizability for stochastic systems are defined in the mean-square sense which play essential roles in the LQ optimal control. By channel/controller co-design, we obtain a sufficient condition ensuring the existence of the mean-square stabilizing solution to the MARE.