Premium
Robust filter design for piecewise discrete‐time systems with time‐varying delays
Author(s) -
Mahmoud Magdi S.,
Xia Yuanqing
Publication year - 2009
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1447
Subject(s) - filter (signal processing) , polytope , control theory (sociology) , piecewise , parametric statistics , filter design , mathematics , piecewise linear function , convex optimization , discrete time and continuous time , mathematical optimization , linear matrix inequality , parametrization (atmospheric modeling) , bounded function , regular polygon , computer science , control (management) , mathematical analysis , statistics , physics , geometry , computer vision , radiative transfer , discrete mathematics , quantum mechanics , artificial intelligence
Abstract A novel delay‐dependent filtering design approach is developed for a class of linear piecewise discrete‐time systems with convex‐bounded parametric uncertainties and time‐varying delays. The time‐delays appear in the state as well as the output and measurement channels. The filter has a linear full‐order structure and guarantees the desired estimation accuracy over the entire uncertainty polytope. The desired accuracy is assessed in terms of either ℋ ∞ ‐performance or ℒ 2 –ℒ ∞ criteria. A new parametrization procedure based on a combined Finsler's Lemma and piecewise Lyapunov–Krasovskii functional is established to yield sufficient conditions for delay‐dependent filter feasibility. The filter gains are determined by solving a convex optimization problem over linear matrix inequalities. In comparison to the existing design methods, the developed methodology yields the least conservative measures since all previous overdesign limitations are almost eliminated. By means of simulation examples, the advantages of the developed technique are readily demonstrated. Copyright © 2009 John Wiley & Sons, Ltd.