Stochastic mixed impulsive control and stability for stochastic functional differential systems with semi-Markov jump

Abstract

This paper focuses on the problem of stochastic mixed impulsive control and stability for stochastic functional differential systems with semi-Markov jump. A new definition of average stochastic impulsive gain is formulated to estimate the stochastic mixed impulsive intensity. Functional systems states are referred to the historical system states in the past time interval rather than in the past time instant of the current time instant. The stability analysis is carried out based on the constructed appropriate Lyapunov functional, Dupire functional Itô’s formula, stochastic analysis theory and graph theory techniques. Moreover, we provide some exponential stability criteria for the investigated systems, which have close relation to not only the topological structures and semi-Markov jump of the functional systems but also average stochastic impulsive gain and stochastic disturbance intensity. Further we put it into practice of a new class of stochastic oscillators systems with semi-Markov jump and the corresponding numerical simulations results are on show to demonstrate the validity of the derived theoretical results.