Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via LaSalle-Yoshizawa-type theorem

ABSTRACT

This paper deals with the decentralised output feedback stabilisation problem for a class of large-scale stochastic time-delay nonlinear systems. A general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time-delay systems. In addition, a stochastic version of the well-known LaSalle-Yoshizawa theorem with time-varying delay is initially proposed for the controller design and stability analysis. Then, for a class of large-scale stochastic systems with time-varying delays, totally decentralised adaptive delay-dependent controllers are designed by using K-filter and backstepping approach. Via LaSalle-Yoshizawa-type theorem and constructing a general Lyapunov function, it is shown that all signals in the closed-loop system are bounded almost surely and the solution is almost surely asymptotically stable. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.

Keywords:

• decentralised stabilisation
• stochastic systems
• LaSalle-Yoshizawa-type theorem
• output feedback
• time-delay

Acknowledgements

This work was supported by the National Natural Science Foundation of PR China under Grants 61174038, 61203048, 61374153, 61374087, the Program for Changjiang Scholars and Innovative Research Team in University under Grant IRT13072, a project funded by the priority academic program development of Jiangsu Higher Education Institutions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The National Natural Science Foundation of PR China [grant number 61174038], [grant number 61203048], [grant number 61374153], [grant number 61374087]; the Program for Changjiang Scholars and Innovative Research Team in University [grant number IRT13072].