Parameter-dependent and filter design for linear systems with arbitrarily time-varying parameters in polytopic domains
- 作者：R.A. Borges ; V.F. Montagner ; R.C.L.F. Oliveira ; P.L.D. Peres ; P.-A. Bliman
- 关键词：Filtering problem ; Linear parameter-varying systems ; ve&_udi=B6V18-4RR8YMB-1&_mathId=mml36&_user=1067359&_cdi=5668&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=
- 刊名：Signal Processing
- 出版年：2008
- 期刊代码：162_01651684
- 类别：et
- 出版时间：July 2008
- 卷：88
- 期：7
- 页码：1801-1816
- 文件大小：320 K
摘要
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 ve&_udi=B6V18-4RR8YMB-1&_mathId=mml30&_user=1067359&_cdi=5668&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=813c002cfa8e2a24b5316d1f1afb7852">
or to the ve&_udi=B6V18-4RR8YMB-1&_mathId=mml31&_user=1067359&_cdi=5668&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=3e3824420c50600de55dc66ada29c0de">
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 ve&_udi=B6V18-4RR8YMB-1&_mathId=mml32&_user=1067359&_cdi=5668&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=190a89d3f46ad7e118c2dafbb663f8cc">
or the ve&_udi=B6V18-4RR8YMB-1&_mathId=mml33&_user=1067359&_cdi=5668&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=3d71f464ecbdab808d49c2540643db57">
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 ve&_udi=B6V18-4RR8YMB-1&_mathId=mml34&_user=1067359&_cdi=5668&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=7062f4323f1f73abeb01ab2e2cb36226">
or the ve&_udi=B6V18-4RR8YMB-1&_mathId=mml35&_user=1067359&_cdi=5668&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=ac5b3aac20389c172323594d611e5905">
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.