High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains

This paper proposes a high-gain observer design for nonlinear systems with delayed output measurements using time-varying gains. The proposed observer is endowed with an exponential stability guarantee and relies on the generalization of the Halanay-type inequalities. We establish that the estimated state and the adapted gain are exponentially bounded and prevent the oscillatory response of the estimates. The time-varying gain feature limits the constant high-gain values of the standard high-gain observer design to the minimum gain required to achieve stability. Furthermore, we derive an explicit relation between the maximum bound of the delay and the maximum gain parameter by using a Lyapunov-Krasovskii functional jointly with the time-varying Halanay inequality. Finally, a comparison with the standard high-gain observer is provided through numerical simulations to demonstrate the superiority of the proposed high-gain observer in rejecting the noise and reducing the peaking phenomena.