Open AccessRobust H 2 and H ∞ filtering for discrete‐time uncertain Linear fractional transform systems
Author(s) -
Sadeghzadeh Arash
Publication year - 2015
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.2014.0381
Subject(s) - linear fractional transformation , mathematics , linear matrix inequality , ellipsoid , parametric statistics , robust control , control theory (sociology) , linear system , mathematical optimization , quadratic equation , filter (signal processing) , convex optimization , lyapunov function , discrete time and continuous time , regular polygon , nonlinear system , computer science , control (management) , physics , quantum mechanics , artificial intelligence , mathematical analysis , statistics , geometry , astronomy , computer vision
This study is concerned with the problem of robust H 2 and H ∞ filtering for uncertain discrete‐time linear systems. Two types of time‐invariant parametric uncertainty, namely polytopic and ellipsoidal, are considered and represented by a linear fractional transformation structure. Obtained auxiliary variables by a convex optimisation problem, play the role of decoupling the Lyapunov variables and the robust filter parameters, in order to cast the problem into a linear matrix inequality‐based optimisation problem. The design conditions are derived based on the quadratic separation concept and employing appropriate parameterisations for the corresponding set of multipliers. The merit of the methods presented in this study lies in their less conservatism than the existing methods for the polytopic uncertain systems, as well as presenting a new convex optimisation procedure for the robust filtering for the ellipsoidal uncertain systems.