Sampled-data based observer design for nonlinear systems with output distributed delay

Abstract

Existing observers that accommodate distributed-delays are mainly designed for linear systems with continuous-time output measurements. In this paper, we seek sampled-measurements-based observers for nonlinear systems with strict-feedback globally Lipschitz dynamics and distributed-delay. Invoking the high-gain principle, we design two observers operating with sampled output measurements. In both, the delay effect is compensated for by using distributed output-predictors. The first observer involves an intersample predictor and its exponential convergence is established using a quadratic Lyapunov function. The second observer involves a zero-order-hold predictor and the exponential convergence is proved using a Lyapunov–Krasovskii functional. To the author’s knowledge, it is the first time that an exponentially convergent observer is developed for nonlinear systems with output distributed-delay and sampled output measurements.