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Article: Induced l2 and generalized H2 filtering for systems with repeated scalar nonlinearities
Title | Induced l2 and generalized H2 filtering for systems with repeated scalar nonlinearities |
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Authors | |
Keywords | Diagonally dominant matrix Generalized H2 performance Induced l2 performance Linear matrix inequality Recurrent neural networks Repeated scalar nonlinearity |
Issue Date | 2005 |
Publisher | IEEE. |
Citation | Ieee Transactions On Signal Processing, 2005, v. 53 n. 11, p. 4215-4226 How to Cite? |
Abstract | This paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks. Both induced l2 and generalized H2 indexes are introduced to evaluate the filtering performance. For a given stable discrete-time systems with repeated scalar nonlinearities, our purpose is to design a stable full-order or reduced-order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l2 or generalized H2 performance. Sufficient conditions are obtained for the existence of admissible filters. Since these conditions involve matrix equalities, the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities, which can be readily solved by using standard numerical software. If these conditions are feasible, a desired filter can be easily constructed. These filtering results are further extended to discrete-time systems with both state delay and repeated scalar nonlinearities. The techniques used in this paper are very different from those used for previous controller synthesis problems, which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix. A numerical example is provided to show the applicability of the proposed theories. © 2005 IEEE. |
Persistent Identifier | http://hdl.handle.net/10722/44929 |
ISSN | 2023 Impact Factor: 4.6 2023 SCImago Journal Rankings: 2.520 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Gao, H | en_HK |
dc.contributor.author | Lam, J | en_HK |
dc.contributor.author | Wang, C | en_HK |
dc.date.accessioned | 2007-10-30T06:13:41Z | - |
dc.date.available | 2007-10-30T06:13:41Z | - |
dc.date.issued | 2005 | en_HK |
dc.identifier.citation | Ieee Transactions On Signal Processing, 2005, v. 53 n. 11, p. 4215-4226 | en_HK |
dc.identifier.issn | 1053-587X | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/44929 | - |
dc.description.abstract | This paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks. Both induced l2 and generalized H2 indexes are introduced to evaluate the filtering performance. For a given stable discrete-time systems with repeated scalar nonlinearities, our purpose is to design a stable full-order or reduced-order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l2 or generalized H2 performance. Sufficient conditions are obtained for the existence of admissible filters. Since these conditions involve matrix equalities, the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities, which can be readily solved by using standard numerical software. If these conditions are feasible, a desired filter can be easily constructed. These filtering results are further extended to discrete-time systems with both state delay and repeated scalar nonlinearities. The techniques used in this paper are very different from those used for previous controller synthesis problems, which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix. A numerical example is provided to show the applicability of the proposed theories. © 2005 IEEE. | en_HK |
dc.format.extent | 416204 bytes | - |
dc.format.extent | 1802 bytes | - |
dc.format.extent | 2200 bytes | - |
dc.format.extent | 10566 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.format.mimetype | text/plain | - |
dc.format.mimetype | text/plain | - |
dc.format.mimetype | text/plain | - |
dc.language | eng | en_HK |
dc.publisher | IEEE. | en_HK |
dc.relation.ispartof | IEEE Transactions on Signal Processing | en_HK |
dc.rights | ©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. | - |
dc.subject | Diagonally dominant matrix | en_HK |
dc.subject | Generalized H2 performance | en_HK |
dc.subject | Induced l2 performance | en_HK |
dc.subject | Linear matrix inequality | en_HK |
dc.subject | Recurrent neural networks | en_HK |
dc.subject | Repeated scalar nonlinearity | en_HK |
dc.title | Induced l2 and generalized H2 filtering for systems with repeated scalar nonlinearities | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1053-587X&volume=53&issue=11&spage=4215&epage=4226&date=2005&atitle=Induced+l/sub+2/+and+generalized+H/sub+2/+filtering+for+systems+with+repeated+scalar+nonlinearities | en_HK |
dc.identifier.email | Lam, J:james.lam@hku.hk | en_HK |
dc.identifier.authority | Lam, J=rp00133 | en_HK |
dc.description.nature | published_or_final_version | en_HK |
dc.identifier.doi | 10.1109/TSP.2005.857009 | en_HK |
dc.identifier.scopus | eid_2-s2.0-27744535823 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-27744535823&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 53 | en_HK |
dc.identifier.issue | 11 | en_HK |
dc.identifier.spage | 4215 | en_HK |
dc.identifier.epage | 4226 | en_HK |
dc.identifier.isi | WOS:000232838900015 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Gao, H=7402971422 | en_HK |
dc.identifier.scopusauthorid | Lam, J=7201973414 | en_HK |
dc.identifier.scopusauthorid | Wang, C=8337851300 | en_HK |
dc.identifier.issnl | 1053-587X | - |