Open AccessDelay‐dependent robust ℋ ∞ filter design for state‐delayed discrete‐time linear systems via homogeneous polynomial matrices
Author(s) -
Lacerda Márcio J.,
Leite Valter J.S.,
Oliveira Ricardo C.L.F.,
Peres Pedro L.D.
Publication year - 2013
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2012.0682
Subject(s) - control theory (sociology) , linear matrix inequality , mathematics , homogeneous polynomial , filter design , filter (signal processing) , lti system theory , polynomial , robust control , discrete time and continuous time , homogeneous , linear system , mathematical optimization , computer science , matrix polynomial , control system , control (management) , engineering , statistics , mathematical analysis , electrical engineering , artificial intelligence , computer vision , combinatorics
This study presents new robust linear matrix inequality (LMI) conditions for robust ℋ ∞ full‐order filter design of discrete‐time linear systems affected by time‐invariant uncertainty and a time‐varying state delay. Thanks to the use of a larger number of slack variables, the proposed robust LMI conditions contain and generalise other results from the literature. LMI relaxations based on homogeneous polynomial matrices of arbitrary degree are used to determine the state‐space realisation of the full‐order filter, that can also be implemented with delayed state terms whenever the time‐delay is available in real time. As another contribution, an iterative LMI‐based procedure involving the decision variables is proposed to improve the ℋ ∞ filter performance. Numerical experiments illustrate the better performance of the proposed filter when compared to other approaches available in the literature.