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Abstract
In this article, we propose an observer for a class of Lipschitz nonlinear systems affected by time-varying and known measurement delays, which is an improvement of the one presented by Cacace <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> ., 2014. Under the assumption that the delay function is piecewise continuous and differentiable, we prove that exponential convergence to zero of the observation error can be achieved with any desired decay rate, by suitably tuning a gain vector. The delay bound achieved with the observer proposed here is less conservative than the one obtained by Cacace <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2014, as confirmed by numerical tests. For the sake of brevity, in this article, only one-step observers are considered. However, a cascade observer can be arranged to cope with arbitrarily long delays.
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