Optimal regulation of linear discrete-time systems with multiplicative noises

This paper studies optimal regulation problem for networked linear discrete-time systems with fading channel. The uncertainties in fading channels are modeled as multiplicative noises. The regulation performance is measured by a quadratic function. The optimal state feedback is designed by the mean-square stabilization solution to a modified Algebraic Riccati equation (MARE). The necessary and sufficient condition to the existence of the mean-square stabilization is presented in terms of the inherent characterizations of the systems. It is a nature extension for the result in standard optimal discrete-time linear quadratic regulation (LQR) problem. We also show that this optimal state feedback design problem is an eigenvalue problem (EVP). And then a design algorithm is developed for this optimal control problem.