Stability Theory of Stochastic Difference Systems

Abstract

This chapter discusses the stability theory of stochastic difference systems. A stochastic difference system is one in which one or more variables can change stochastically at discrete instants of time. Stochastic difference systems are the stochastic versions of deterministic discrete time systems. The class of stochastic difference systems includes most modern industrial and military control systems, for they invariably include some elements whose inputs or outputs are discrete in time. Examples of such elements are digital computers, pulsed radar units, and coding units in most communication systems. One of the most important qualitative properties of stochastic difference systems is the stability of such systems. The chapter presents criteria for stability of linear and nonlinear stochastic difference systems. It highlights the relationship between various stability definitions is shown. The chapter also discusses properties peculiar to linear systems are also discussed. Various special methods have been devised for the study of the stability of stochastic differential equations.