On high-gain observer design for nonlinear systems with delayed output measurements

In this paper, we propose a high-gain observer design for nonlinear systems with time-varying delayed output measurements. Based on a recent high-gain like observer design method, called HG/LMI observer, a larger bound of the time-delay is allowed compared to that obtained by using the standard high-gain methodology. Such a HG/LMI observer adopts a lower value of the tuning parameter, which results in the reduction of the value of the observer gain, and an increase in the maximum bound of the delay required to ensure exponential convergence. Indeed, an explicit relation between the maximum bound of the delay and the observer tuning parameter is derived by using a Lyapunov-Krasovskii functional jointly with the Halanay inequality. Such a relation shows clearly the superiority of HG/LMI observer design methodology. An application to nonlinear systems with sampled measurements is provided. Furthermore, the proposed methodology is extended to systems with nonlinear outputs. This extension provides more general synthesis conditions and encompasses the linear case as a particular situation. Finally, two numerical examples are proposed to illustrate the performance of the proposed observer design procedure, and comparison to standard approaches is also provided. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a high-gain observer design method is proposed for nonlinear systems with time-varying delayed output measurements. The HG/LMI observer allows for a larger bound of the time-delay compared to the standard high-gain methodology, and it adopts a lower tuning parameter value. The proposed methodology provides more general synthesis conditions and can be applied to systems with nonlinear outputs.