Stabilization of nonlinear hybrid stochastic delay systems by feedback control based on discrete-time state and mode observations

ABSTRACT

This paper is concerned with the stabilization problem for nonlinear stochastic delay systems with Markovian switching by feedback control based on discrete-time state and mode observations. By constructing an efficient Lyapunov functionals, we establish the sufficient stabilization criteria not only in the sense of exponential stability (both the mean-square stability and the almost sure stability) but also in other sense – that of $H_{\mathrm{\infty }}$ stability and asymptotic stability. Meanwhile, the upper bound on the duration τ between two consecutive state and mode observations is obtained. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.

Keywords:

• Hybrid stochastic delay systems
• stabilization
• feedback control
• discrete-time state and mode
• Lyapunov functional

2010 Mathematics Subject Classification:

• Stochastic stability

Acknowledgments

The authors would like to thank for the financial support by the Initial Research Funds for Young Teachers of Donghua University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors would like to thank for the financial support by the Initial Research Funds for Young Teachers of Donghua University (109-07-0053029).