Entropy stability of continuous dynamic systems

Summarization: The problem of stochastic stability of continuous dynamic systems is examined from the point of view of entropy. The concept of entropy, as it was defined by Shannon, represents a measure of average uncertainty in a random situation. In this research, the entropy of the state of a system is considered and conditions for keeping it within certain bounds or minimizing it are sought. For this purpose several tools and results of the theory of stochastic differential equations are used. Previous results of narrow scope concerned only systems with initial random conditions. Here, the problem is generalized to systems with noise inputs. The systems under consideration are with constant or periodic coefficients. Also, general non-linear Itô-type systems are examined. A linearization procedure is applied in the non-linear case and sufficient conditions for stability are developed. Finally, a lower bound to the entropy of nonlinear systems is found. This bound provides the tools for instability results. It should be stressed that some of the results are weak because of the generality of the criterion used. However, simplicity is their virtue.Presented on: International Journal of Contro