Stabilization via delay feedback for highly nonlinear stochastic time-varying delay systems with Markovian switching and Poisson jump

Abstract

Little work seems to be known about stabilization results of highly nonlinear stochastic time-varying delay systems (STVDSs) with Markovian switching and Poisson jump. This paper is concerned with the stabilization problem for a class of STVDSs with Markovian switching and Poisson jump. The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. The aim of this paper is to design a delay feedback controller to make an unstable highly nonlinear STVDSs with Markovian switching and Poisson jump $H_\infty$-stable and asymptotically stable. Besides, an illustrative example is provided to support the theoretical results.

Keywords

• stochastic systems
• time-varying delay
• delay feedback control
• markovian switching
• poisson jump