Non-fragile H∞ filtering for nonlinear discrete-time delay systems with randomly occurring gain variations

•The H∞ filtering for nonlinear systems instead of linear ones in existing literature is investigated.•Randomly occurring gain variations are taken into account.•Less conservative result is derived for linear systems that are free of randomly occurring gain variations.•Zero inequality is first employed to handle the H∞ filtering problem.

In this paper,the problem of H∞ filtering for a class of nonlinear discrete-time delay systems is investigated. The time delay is assumed to be belonging to a given interval, and the designed filter includes additive gain variations which are supposed to be random and satisfy the Bernoulli distribution. By the augmented Lyapunov functional approach, a sufficient condition is developed to ensure that the filtering error system is asymptotically mean-square stable with a prescribed H∞ performance. In addition, an improved result of H∞ filtering for linear system is also derived. The filter parameters are obtained by solving a set of linear matrix inequalities. For nonlinear systems, the applicability of the developed filtering result is confirmed by a longitudinal flight system, and an additional example for linear system is presented to demonstrate the less conservativeness of the proposed design method.