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

机译：H-Infinity过滤器设计用于有限频域多粒子不确定性的线性时间不变系统

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摘要

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.
机译：本文涉及用于离散时间和连续时间线性系统的有限频率H无限全阶滤波器设计的问题，具有多种子间的不确定性。基于广义的卡尔曼-yakubovich-popov引理和参数依赖的Lyapunov函数，在矩阵不等式方面建立了一组足够的条件，确保过滤误差系统是稳定的，并且H无限衰减水平从干扰到估计误差，小于外部干扰的规定的有限频域上的给定值。然后，为了线性化和放松所获得的矩阵不等式，我们通过两次应用Finsler的Lemma引入大量的松弛变量，这在优化保证的H无限距离性能方面提供了额外的自由度。这导致解决方案中的性能提高和减少保守主义。稍后示出了通过求解一组线性矩阵不等式来获得强大的过滤器增益。给出了与现有方法相比的所提出的方法的有效性和较少的保守性。版权所有（c）2016 John Wiley＆Sons，Ltd。

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