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.