ABSTRACT
In many applications where dynamical system models are used to describe the behavior of a real world system, stochastic components and random noises are included in the model to capture uncertainties in the operating environment and the system structure of the physical process being studied. The analysis and control of such systems then involves evaluating the stability properties of a random dynamical system. Stability is an important property of a system and we know from classical control theory that input-output stability is a necessary condition for control system design, but are aware that analytic techniques for evaluating stability are often restricted to linear systems, or special classes of nonlinear systems. The general study of the stability properties of stochastic dynamical systems is important and considerable effort has been devoted to the study of stochastic stability. Significant results have been reported in the literature with applications to physical and engineering systems.
