Stabilization of Non-Linear Systems: Information Theoretic vs. Geometric Analysis

In this chapter, we consider non-linear models controlled under information constraints. More specifically, this chapter is concerned with necessary and sufficient conditions on information channels in a networked non-linear stochastic control system for which there exist coding and control policies such that the controlled system is stochastically stable in one or more of the following senses: (i) The state \(\{x_t\}\) and the coding and control parameters lead to a stochastically stable process (in senses to be made precise), and (ii) \(\{x_t\}\) is asymptotically stationary, or asymptotically mean stationary (AMS), and (iii) \(\{x_t\}\) is (asymptotically) ergodic.