Generalized Play-Operator Under Stochastic Perturbations: An Analytic Approach

Abstract

A new class of models of hysteretic converters which generalizes the classical play-operator with stochastic properties (defining curves of this operator are treated as non-deterministic and have a random distribution) is proposed. In this case an output of stochastic converter is defined as a random process. The correctness of the definition of the corresponding converter in terms of a special limit construction is proved. Within this definition an output of the corresponding converter is determined at arbitrary continuous inputs. Properties of introduced converters are investigated and illustrative examples are presented.