Global stabilisation of nonlinear systems with unknown time-varying delay and measurement uncertainty

ABSTRACT

Based on a new constructive solution of a couple of matrix inequalities containing an unknown time-varying parameter, this paper proposes a novel dual-gain scaling approach including a dynamic-gain observer and an output feedback controller with static and dynamic gains. In particular, our control approach is applicable to a class of nonlinear time-delay systems with nonlinear growth constraint and large unknown measurement sensitivity that may be non-differentiable. With the help of the Razuminkhin theorem, it is shown that the global adaptive stability of the resulting closed-loop system is achieved and our controller is robust to arbitrary bounded time-varying delay. In addition, the control approach proposed is non-backstepping and has low computing complexity.

KEYWORDS:

• Nonlinear time-delay systems
• measurement uncertainty
• scaling change
• output feedback

Acknowledgments

The authors would like to thank the editor and all the referees for their constructive and valuable comments, which improved the presentation of this paper.

Disclosure statement

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

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Provincial Universities of Zhejiang (Grant Number GK219909299001-002), the Zhejiang Provincial Natural Science Foundation of China (Grant Number LY21F030008) and the National Natural Science Foundation of China (Grant Number 61703132).