Control of Continuous-Time Linear Gaussian Systems Over Additive Gaussian Wireless Fading Channels: A Separation Principle

This note is concerned with the control of continuous-time linear Gaussian systems over additive white noise wireless fading channels subject to capacity constraints. Necessary and sufficient conditions are derived, for bounded asymptotic and asymptotic observability and stabilizability in the mean square sense, for controlling such systems. For the case of a noiseless time-invariant system controlled over a continuous-time additive white Gaussian noise channel, the sufficient condition for stabilizability and observability states that the capacity of the channel C must satisfy C > Sigma_{{i;Re(lambdai(A))ges0}} Re(lambda_i(A)), where A is the system matrix and lambda_i(A) denotes the eigenvalues of A. The necessary condition states that the channel capacity must satisfy C ges Sigma _{{i;Re(lambdai(A))ges0}} Re(lambda_i(A)). Further, it is shown that a separation principle holds between the design of the communication and the control subsystems, implying that the controller that would be optimal in the absence of the communication channel is also optimal for the problem of controlling the system over the communication channel.