Robust Absolute Stability of lumping Stochastic Systems

Abstract The control systems represented by a finite family of continuous time stochastic models are considered. Each individual model of this family is described by the differential equation of Ito type with parametrical white noise and sector bounded nonlinearities. The discontinuous (jumping) transitions between the individual models is described by a homogeneous Markov chain. An algebraic condition of exponential stability in the mean square of considered system for given parametrical noise intensities, arbitrary nonlinearities of the class above, and arbitrary transition probabilities of the Markov chain are presented. Generalization on the discrete time systems is also given.