State feedback covariance control for linear finite signal-to-noise ratio models

A new model for linear systems, introduced by Skelton (1994), assumes that the intensity of the noise corrupting a signal is proportional to the variance of that signal. In LQG theory, the noise intensity is assumed to be unrelated to the signal. We refer to the new model as the “finite signal-to-noise model” (or FSN model). This paper derives the necessary and sufficient conditions for the existence of a mean square stabilizing state feedback controller for FSN models. The problem is not convex, but an iterative algorithm is proposed which guarantees a solution under mild conditions. The existence conditions provide an explicit lower bound on the signal-to-noise ratios, required for stability. Finally, an input covariance minimization problem is solved numerically