Stabilization of stochastic regime-switching Poisson jump equations by delay feedback control

Autor:	Guangjie Li
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Almost sure exponential stability Markov’s chain Poisson jumps Delay feedback control Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2022, Iss 1, Pp 1-16 (2022)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-022-02756-6
Popis:	Abstract This paper is concerned with the stabilization of stochastic regime-switching Poisson jump equations (also known as stochastic differential equations with Markovian switching and Poisson jumps, abbreviated as SDEwMJs). The aim of this paper is to design a feedback controller with delay δ ( δ > 0 $\delta >0$ ) to make an unstable SDEwMJ become stable. It is proved that the delay δ is bounded by a constant δ̄. Moreover, an implicit lower bound for δ , ¯ $\bar{\delta ,}$ which can be computed numerically, is provided. As a product, the almost sure exponential stability of the controlled SDEwMJ is obtained. Besides, an example is given to demonstrate the theoretical results.
Databáze:	Directory of Open Access Journals
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