Global practical stabilisation of a class of switched nonlinear systems via sampled-data control

ABSTRACT

This paper investigates a global practical stabilisation problem of a class of switched nonlinear systems via sampled-data control, where all the subsystems are assumed to be in non-strict feedback form and all the $z_0$-subsystems are not required to be input-to-state stable. Since the system states are unmeasurable and the output can only be measured at the sampling instants, an observer is designed to estimate the state. By adopting the multiple Lyapunov function method and the backstepping technique, a virtual controller is constructed, then a sampled-data controller is obtained by discretizing the designed virtual controller. With appropriate choice of a switching law and an allowable sampling period, it is proved that the designed sampled-data controller renders the corresponding closed-loop system to be globally practically stable. Finally, two examples are presented to illustrate effectiveness of the proposed methods.

Keywords:

• Switched systems
• nonlinear systems
• sampled-data control
• multiple Lyapunov function method
• backstepping technique

Acknowledgments

We would like to thank Shibaura Institute of Technology, Japan, for supporting the first author's academic visit.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 61873128), and Postgraduate Research and Practice Innovation Program of Jiangsu Province (KYCX 17-0365).