Non-fragile H∞ Filter Design for Delta Operator Formulated Systems with Circular Region Pole Constraints: an LMI Optimization Approach

The problem of non-fragile H∞ filtering for a class of linear systems described by delta operator with circular region pole constraints is investigated. The purpose of the paper is to design a filter such that the error filtering system not only satisfies the prescribed circular pole constraints or D-stability constraint, but also meets the prescribed H∞ norm constraint on the transfer function from the disturbance input to the estimation error. The filter gain to be designed is assumed to have multiplicative gain variations. A sufficient condition for the existence of such a filter is obtained by using appropriate Lyapunov function and linear matrix inequality (LMI) technique. A numerical example is provided to demonstrate the effectiveness and less conservativeness of the proposed design.