Robust <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si26.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si27.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math> filtering for uncertain linear systems
AutomaticaPublished 10 August 2006
Zhisheng Duan, Jingxin Zhang, Cishen Zhang, E. Mosca
Citations307
SJR quartileQ1
SJR score3.05
SNIP2.35
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
An apparatus for reducing wastage during the start-up phase of extrusion device used to produce extruded profiles such as tread strips for vehicle tires from a plurality of mixtures.
Abstract
This paper extends the existing results on the robust H2 and H∞ filtering problems with respect to polytopic uncertainty. A new structure of slack variables is introduced to provide extra free dimensions in the solution space for the H2 and H∞ optimization. This directly leads to performance improvement and reduction of conservativeness in the filtering solution. The method is applicable to both discrete and continuous time systems. Performance of the proposed solutions in comparison with that of the existing methods is illustrated by several examples.
Keywords
Engineering
International Journal of Robust and Nonlinear ControlA linear matrix inequality approach to<i>H</i><sub>∞</sub>control
3,208 Citations1994P. Gahinet, Pierre Apkarian
Systems & Control LettersA new discrete-time robust stability condition
1,509 Citations1999Maurı́cio C. de Oliveira, J. Bernussou +1 more
International Journal of ControlExtended H 2 and H norm characterizations and controller parametrizations for discrete-time systems
731 Citations2002Maurı́cio C. de Oliveira, José C. Geromel +1 more
Systems & Control LettersA new robust -stability condition for real convex polytopic uncertainty
696 Citations2000Dimitri Peaucelle, Denis Arzelier +2 more
IEEE Transactions on Automatic ControlAnalysis and synthesis of robust control systems via parameter-dependent Lyapunov functions
402 Citations1996Éric Féron, Pierre Apkarian +1 more
It is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant, and sufficient conditions for the existence of parameter-dependent Lyapunov functions are given in terms of a criterion reminiscent of Popov's stability criterion.
AutomaticaImproved robust H2 and H∞ filtering for uncertain discrete-time systems
341 Citations2004Lihua Xie, Lilei Lu +2 more
IEEE Transactions on Signal ProcessingOptimal linear filtering under parameter uncertainty
284 Citations1999José C. Geromel
The present case of convex bounded parameter uncertainty, the basic numerical design tools are linear matrix inequality (LMI) solvers instead of the Riccati equation solvers used for the design of robust filters available in the literature to date.
IEEE Transactions on Aerospace and Electronic SystemsReduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities
275 Citations1997Karolos Grigoriadis, James T. Watson
IEEE Transactions on Automatic ControlImproved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty
232 Citations2001U. Shaked
Modifications to the representation of the bounded real lemma (BRL) in the linear continuous time-invariant case are introduced, reducing the overdesign that occurs in the analysis and the design of systems with polytopic-type uncertainties.
SIAM Journal on Control and OptimizationRobust Filtering of Discrete-Time Linear Systems with Parameter Dependent Lyapunov Functions
214 Citations2002José C. Geromel, Maurı́cio C. de Oliveira +1 more
IEEE Transactions on Signal ProcessingRobust and reduced-order filtering: new LMI-based characterizations and methods
205 Citations2001Hoang Duong Tuan, Pierre Apkarian +1 more
New linear matrix inequality (LMI) characterizations of minimum variance or H/sub 2/ performance are derived and demonstrated that they allow the use of parameter-dependent Lyapunov functions while preserving tractability of the problem.
SIAM Journal on Control and Optimization<i>H</i><sub>2</sub> and $H_\infty$ Robust Filtering for Discrete-Time Linear Systems
142 Citations2000José C. Geromel, J. Bernussou +2 more
It is shown that by a suitable change of variables, both design problems can be converted into convex programming problems written in terms of linear matrix inequalities (LMI) and the optimal guaranteed performance H2 and $H_\infty$ filters are proven to be of the same order as the order of the system.
IEEE Transactions on Signal ProcessingRobust mixed ℋ/sub 2//ℋ/sub ∞/ filtering of 2-D systems
112 Citations2002Hoang Duong Tuan, Pierre Apkarian +2 more
This paper deals with several challenging problems of robust filtering for two-dimensional (2-D) systems and new linear matrix inequality (LMI) characterizations for the H∞ and H2 norms of 2-D systems are introduced and thoroughly established.
Systems & Control LettersRobust filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions
93 Citations2004Karina A. Barbosa, Carlos E. de Souza +1 more
Affine parameter-dependent Lyapunov functions for real parametric uncertainty
73 Citations2002P. Gahinet, Pierre Apkarian +1 more
IEEE Transactions on Signal ProcessingL/sub 2/ optimal filter reduction: a closed-loop approach
23 Citations1998Lihua Xie, Wei‐Yong Yan +1 more
This paper is concerned with the problem of order reduction of a full-order Kalman filter for a stable linear signal model so that the steady-state filtering error variance associated with the reduced order filter is minimized.