Asymptotic stability in distribution of stochastic systems with semi-Markovian switching

ABSTRACT

This paper investigates the asymptotic stability in distribution of stochastic systems with semi-Markovian switching whose transition rates are time varying, which are more general than stochastic systems with Markovian switching. Some sufficient conditions for the asymptotic stability in distribution of stochastic systems with semi-Markovian switching are established and those conditions are employed to design the state-feedback controllers in terms of linear matrix inequalities. Finally, several examples are given to illustrate the effectiveness of the theoretical results.

KEYWORDS:

• Stochastic systems with semi-Markovian switching
• asymptotic stability in distribution
• transition rate
• linear matrix inequality

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was jointly supported by the National Natural Science Foundation of China [grant number 61773217, 61374080, 11531006]; the Natural Science Foundation of Jiangsu Province [grant number BK20161552]; Qing Lan Project of Jiangsu Province; the Priority Academic Program Development of Jiangsu Higher Education Institutions; the Natural Science Foundation for Colleges and Universities in Jiangsu Province [grant number 14KJB110025].