Fault Estimation for Discrete-Time Systems With Lipschitz Perturbation and Time-Variant Coefficients

Abstract

This brief investigates the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fault estimation problem for a class of Lipschitz nonlinear systems with timevariant coefficient matrices in discrete-time settings. By introducing an auxiliary unknown input based on the nonlinear term, a quasi-linear model and its corresponding indefinite quadratic performance function for fault estimation are respectively given in lieu of the original nonlinear dynamics and the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance metric, such that the estimation problem is converted as an indefinite optimization problem. By artificially constructing a Krein-space based dynamic model, the classical linear estimation technique in H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> sense is employed to seek a suitable choice of the estimation of the fault. A condition that ensures the existence of the estimator is derived analytically. A Kalman-filter-like estimator recursion is proposed simultaneously.