Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates

  • Authors:

  • Girish N. Nair;Robin J. Evans

  • Affiliations:

  • -;-

  • Venue:
  • SIAM Journal on Control and Optimization
  • Year:
  • 2004

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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. Analogously 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 time-invariant 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 arguments employing the entropy power inequality of information theory, and a new quantizer error bound, an explicit expression for the infimum stabilizing data rate is derived, under very mild conditions on the initial state and noise probability distributions.