Stabilization of a class of uncertain feedforward nonlinear systems subject to input delay

ABSTRACT

This note presents nested-saturation controllers for stabilising a class of feed-forward nonlinear systems that are subject to uncertain gains and an input delay. To verify the reduction of nested saturations, we adopt the strategy of partitioning the delay-interval, and can thus use the state values in a small domain to calculate a crucial composite term; when proving the asymptotic stability of the reduced time-delay system, we utilise the nested structure of saturations to make a coordinate transformation and consequently, can use a M-matrix based stability criterion. In this way, the analysis in two stages is straightforward, and a single group of parameter conditions are summarised to guarantee the global asymptotic stability of the closed-loop system.

Keywords:

• Stabilisation
• uncertain nonlinear systems
• input delay
• saturated control

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under grant no. 61374024, and the Hunan Provincial Natural Science Foundation of China (2020JJ4755).

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61374024], and the Hunan Provincial Natural Science Foundation of China [grant number 2020JJ4755].

Notes on contributors

Jun Liu

Jun Liu received the B.S. degree in automation and the M.S. degree in control theory and control engineering from China University of Geosciences, Wuhan, China,in 2007 and 2010 respectively. He is currently pursuing the Ph.D. degree in Control Science and Engineering from Central South University, Changsha, China. His main research interests include uncertain nonlinear systems and saturated control.

Huawen Ye

Huawen Ye received his Ph.D. degree in Control Science and Engineering from Northwestern Polytechnical University, Xi'an, China, in 2002. He is currently a professor at the School of Automation, Central South University. His research interests include nonlinear control systems and networked control systems.

Xianting Qi

Xianting Qi received the B. S. degree in the Department of Automation from Wuhan University of Technology, Wuhan, China, in 2018. She is currently pursuing the M. S. degree in Control Engineering from Central South University, Changsha, China. Her current research interests include saturated control.