H∞ filter design for linear time-invariant systems with polytopic uncertainties in finite frequency domain

This paper deals with the problem of finite frequency H infinity full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman-Yakubovich-Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H infinity attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H infinity performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. Copyright (c) 2016 John Wiley & Sons, Ltd.