Polynomially parameter-dependent approach of robust H∞ filter for polytopic delta operator systems

The problem of robust H_∞ filtering for polytopic Delta operator systems is investigated. An enhanced linear matrix inequality (LMI) representation for H_∞ performance criterion is presented based on the bounded real lemma by introducing two slack matrices. Upon this criterion, a structured polynomially parameter-dependent approach is proposed to solve robust H_∞ filtering problem, which is realized by carefully selecting the structure of the matrices involved in the products with system matrices. An LMI condition is obtained for the existence of admissible filters, and the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. The effectiveness of the proposed design is demonstrated in a numerical example.