Stabilisation in distribution by delay feedback control for stochastic differential equations with Markovian switching and Lévy noise

Abstract

This paper is devoted to the stability in distribution of stochastic differential equations with Markovian switching and Lévy noise by delay feedback control. By constructing efficient Lyapunov functional and linear delay feedback controls, the stability in distribution of stochastic differential equations with Markovian switching and Lévy noise is accomplished with the coefficients satisfying globally Lipschitz continuous. Moreover, the design methods of feedback control under two structures of state feedback and output injection are discussed. Finally, a numerical experiment and new algorithm are provided to sustain the new results.

Delay-Independent Stability of Stochastic Systems with Time-Varying Delay and Lévy Noise

“…Therefore, in practical situations, it is more appropriate to use Lévy noise to simulate large external and/or internal fluctuations. For example, experts often use Lévy noise to simulate large-scale external or internal disturbances in financial markets [3,4]. In recent years, many valuable theoretical and application results have been provided on stability for stochastic differential systems with Lévy noise [5,6].…”

Stabilisation in distribution of hybrid ordinary differential equations by periodic noise

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