Parameter-dependent H2 and H∞ filter design for linear systems with arbitrarily time-varying parameters in polytopic domains

Authors:
R. A. Borges;V. F. Montagner;R. C. L. F. Oliveira;P. L. D. Peres;P. -A. Bliman
Affiliations:
School of Electrical and Computer Engineering, University of Campinas, CP 6101, 13.083-970 Campinas, SP, Brazil;CT Alegrete/UNIPAMPA-GEPOC/UFSM, Alegrete, RS, Brazil;School of Electrical and Computer Engineering, University of Campinas, CP 6101, 13.083-970 Campinas, SP, Brazil;School of Electrical and Computer Engineering, University of Campinas, CP 6101, 13.083-970 Campinas, SP, Brazil;INRIA, Rocquencourt, France
Venue:
Signal Processing
Year:
2008

Citing 10
Cited 7

Linear robust control

Linear robust control
Robust H∞ -filtering design with pole placement constraint via linear matrix inequalities

Journal of Optimization Theory and Applications
A linear matrix inequality approach to the design of robust H2 filters

Advances in linear matrix inequality methods in control
A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters

SIAM Journal on Control and Optimization
Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness

SIAM Journal on Matrix Analysis and Applications
Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs

Mathematical Programming: Series A and B
Filter design for LPV systems using quadratically parameter-dependent Lyapunov functions

Automatica (Journal of IFAC)
Robust and reduced-order filtering: new LMI-based characterizationsand methods

IEEE Transactions on Signal Processing
Optimal linear filtering under parameter uncertainty

IEEE Transactions on Signal Processing
Brief Robust filtering with guaranteed energy-to-peak performance - an LMI approach

Automatica (Journal of IFAC)

Deconvolution filtering for stochastic systems via homogeneous polynomial Lyapunov functions

Signal Processing
New delay-dependent L2-L∞ filter design for stochastic time-delay systems

Signal Processing
H∞ filtering of time-delay T-S fuzzy systems based on piecewise Lyapunov-Krasovskii functional

Signal Processing
H∞ filtering for discrete-time linear systems with bounded time-varying parameters

Signal Processing
H∞ filtering for singular systems with communication delays

Signal Processing
Robust H2 and H∞ filter design for uncertain linear systems via LMIs and polynomial matrices

Signal Processing
Relaxed filtering designs for continuous-time nonlinear systems via novel fuzzy H∞ filters

Signal Processing

Quantified Score

Hi-index	0.08

Visualization

Abstract

In this paper, the problem of filter design for linear continuous-time systems with arbitrarily fast time-varying parameters is investigated. The time-varying parameters belong to a polytope with known vertices, affect all the system matrices and are assumed to be available online for implementation of the filters. Necessary and sufficient parameter-dependent linear matrix inequality (LMI) conditions for the existence of a parameter-dependent filter assuring that the estimation error dynamics is quadratically stable and satisfies bounds to the H"2 or to the H"~ norms are given. A sequence of standard LMI conditions assuring the existence of homogeneous polynomially parameter-dependent (HPPD) solutions to the parameter-dependent LMIs for filter design is provided in terms of the vertices of the polytope (no gridding is required), yielding parameter-dependent filters of arbitrary degree assuring quadratic stability of the error dynamics for the H"2 or the H"~ cases. As the degree of the HPPD solutions increases, less and less conservative LMI conditions are obtained, tending to the necessary conditions that assure optimal values for the H"2 or the H"~ performance of the estimation error dynamics under quadratic stability. Numerical examples illustrate the results, showing that parameter-dependent filters can provide better attenuation levels than the ones obtained with robust filters, at the price of a more complex filtering strategy.