Observer for a class of Lipschitz nonlinear systems with multiple time‐varying delays in the nonlinear measured outputs

Abstract

This paper provides a novel chain observer for a class of Lipschitz nonlinear systems where the nonlinear measured outputs are corrupted by multiple time‐varying long delays. The main contribution is to synthesize a chain observer for a wider class of Lipschitz nonlinear systems with multiple outputs (described by Lipschitz nonlinear functions) with long time‐varying delays. In the design of the proposed observation scheme, the provided observer is comprised of a chain of state observers, where each one has a similar structure. Each observer is tasked to estimate the state over a short time horizon, whereas the first item of the chain provides the actual state estimation. Moreover, each item of the chain observer furnishes a proportional‐integral dynamical term which allows to compensate for the time‐delay effect. The observer gains are obtained from the solution of a set of delay‐dependent Linear Matrix Inequalities (LMIs), which is based on less restrictive LMI synthesis conditions. The convergence analysis relies on a Lyapunov–Krasovskii functional, which demonstrates that the observation error decays to zero. Numerical examples are given, in order to highlight the effectiveness of the provided observer.

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