Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates

Abstract. Feedback control with limited data rates is an emerging area which incorporates ideas from both control and information theory. A fundamental question it poses is how low the closed loop data rate can be made before a given dynamical system is impossible to stabilize by any coding and control law. Analagously to source coding, this defines the smallest error-free data rate sufficient to achieve “reliable ” control, and explicit expressions for it have been derived for linear timeinvariant systems without disturbances. In this paper, the more general case of finite-dimensional linear systems with process and observation noise is considered, the object being mean square state stability. By inductive…