LQG control of LTI systems with random input and output gains

In this paper, the Linear Quadratic Gaussian (LQG) control of linear time invariant (LTI) systems with random input and output gains is studied. One main novelty of this work is that we study the problem under the framework of channel/controller co-design which allows the control designer to have the additional freedom to design the communication channels. With the channel/controller co-design, the optimal control problem studied is feasible if and only if the system is mean-square stabilizable and detectable. Moreover, we show that the separation principle partially holds under the TCP-like protocols. The optimal controller is an estimated state feedback, combining the optimal state feedback design and the optimal state estimation design. However, there exists certain asymmetry. The optimal state feedback gain does not depend on the estimator design, while the optimal estimator does depend on the optimal state feedback gain.