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

This brief investigates the $H_{\infty }$ fault estimation problem for a class of Lipschitz nonlinear systems with time-variant 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 $H_{\infty }$ 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 $H_{2}$ 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.