Observer Design for Nonlinear Systems with Output Distributed Delay

Abstract

So far, the problem of observer design in the presence of output distributed-delays has only been investigated in the case of linear systems. In this paper, we present a new observer that applies for a class of nonlinear systems including strict-feedback Lipschitz nonlinear dynamics. The combined difficulties of system nonlinearity and distributed-delay are respectively dealt with by using the high-gain principle and a distributed output-predictor, which is a key component of the observer. Exponential stability of the resulting state estimation error system is analyzed using Lyapunov stability tools. We show that exponential stability is ensured for not too large delay and the maximal admissible delay size depends on the system nonlinearity: the stronger the nonlinearity the smaller the maximal admissible delay. To the author’s knowledge, it is the first time that an exponentially convergent observer is developed for nonlinear systems with output distributed-delay.