{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T13:55:43Z","timestamp":1761486943435},"reference-count":51,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[1991,7,1]],"date-time":"1991-07-01T00:00:00Z","timestamp":678326400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Automatica"],"published-print":{"date-parts":[[1991,7]]},"DOI":"10.1016\/0005-1098(91)90057-9","type":"journal-article","created":{"date-parts":[[2003,3,14]],"date-time":"2003-03-14T13:27:27Z","timestamp":1047648447000},"page":"663-676","source":"Crossref","is-referenced-by-count":28,"title":["On identification of stable systems and optimal approximation"],"prefix":"10.1016","volume":"27","author":[{"given":"P.M.","family":"M\u00e4kil\u00e4","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/0005-1098(91)90057-9_BIB1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01075356","article-title":"Infinite Hankel matrices and generalized Caratheodory-Fejer and Riesz problems","volume":"2","author":"Adamjan","year":"1968","journal-title":"Funct Anal Applic"},{"key":"10.1016\/0005-1098(91)90057-9_BIB2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1070\/SM1971v015n01ABEH001531","article-title":"Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem","volume":"15","author":"Adamjan","year":"1971","journal-title":"Math. USSR Sbornik"},{"key":"10.1016\/0005-1098(91)90057-9_BIB3","doi-asserted-by":"crossref","first-page":"695","DOI":"10.2307\/2373069","article-title":"Mean convergence of expansions in Laguerre and Hermite series","volume":"87","author":"Askey","year":"1965","journal-title":"Am. J. Math."},{"key":"10.1016\/0005-1098(91)90057-9_BIB4","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0005-1098(71)90059-8","article-title":"System identification\u2014a survey","volume":"7","author":"\u00c5str\u00f6m","year":"1971","journal-title":"Automatica"},{"key":"10.1016\/0005-1098(91)90057-9_BIB5","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0167-6911(89)90098-4","article-title":"On the L\u221e consistency of L2 estimators","volume":"12","author":"Caines","year":"1989","journal-title":"Syst. Control Lett."},{"key":"10.1016\/0005-1098(91)90057-9_BIB6","author":"Chandrasekharan","year":"1989"},{"key":"10.1016\/0005-1098(91)90057-9_BIB7","author":"Coughanowr","year":"1965"},{"key":"10.1016\/0005-1098(91)90057-9_BIB8","author":"Deshpande","year":"1981"},{"key":"10.1016\/0005-1098(91)90057-9_BIB9","volume":"Vol. 2","author":"Erd\u00e9lyi","year":"1953"},{"key":"10.1016\/0005-1098(91)90057-9_BIB10","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0167-6911(87)90004-1","article-title":"H\u221e minimization for delay systems","volume":"9","author":"Flamm","year":"1987","journal-title":"Syst. Control Lett."},{"key":"10.1016\/0005-1098(91)90057-9_BIB11","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1137\/0325038","article-title":"On the H\u221e-optimal sensitivity problem for systems with delays","volume":"25","author":"Foias","year":"1987","journal-title":"SIAM J. Control Optimiz."},{"key":"10.1016\/0005-1098(91)90057-9_BIB12","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1137\/0519072","article-title":"Some explicit formulae for the singular values of certain Hankel operators with factorizable symbol","volume":"19","author":"Foias","year":"1988","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/0005-1098(91)90057-9_BIB13","article-title":"Approximation of delay systems\u2014A case study","author":"Glader","year":"1989"},{"key":"10.1016\/0005-1098(91)90057-9_BIB14","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1137\/0326049","article-title":"Realisation and approximation of linear infinite-dimensional systems with error bounds","volume":"26","author":"Glover","year":"1988","journal-title":"SIAM J. Control Optimiz."},{"key":"10.1016\/0005-1098(91)90057-9_BIB15","series-title":"Proc. 25th IEEE Conf. on Decision and Control","article-title":"Balanced realisation and Hankel-norm approximation of systems involving delays","author":"Glover","year":"1986"},{"key":"10.1016\/0005-1098(91)90057-9_BIB16_1","article-title":"Rational approximation of a class of infinite-dimensional systems","author":"Glover","year":"1988"},{"key":"10.1016\/0005-1098(91)90057-9_BIB16_2","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02551374","article-title":"Part I: Singular values of Hankel operators","volume":"4","author":"Glover","year":"1990","journal-title":"Math. Control Signals Syst."},{"key":"10.1016\/0005-1098(91)90057-9_BIB17","series-title":"Modeling, Robustness and Sensitivity Reduction in Control Systems","article-title":"Bounds on the achievable accuracy in model reduction","volume":"vol. F34","author":"Glover","year":"1987"},{"key":"10.1016\/0005-1098(91)90057-9_BIB18","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/0005-1098(80)90076-X","article-title":"Correlation methods","volume":"16","author":"Godfrey","year":"1980","journal-title":"Automatica"},{"key":"10.1016\/0005-1098(91)90057-9_BIB19","author":"Gohberg","year":"1969"},{"key":"10.1016\/0005-1098(91)90057-9_BIB20","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1109\/9.24229","article-title":"Approximation of infinite dimensional systems","volume":"AC-34","author":"Gu","year":"1989","journal-title":"IEEE Trans. Aut. Control"},{"key":"10.1016\/0005-1098(91)90057-9_BIB21","series-title":"Computational and Combinatorial Methods in Systems Theory","article-title":"Hankel norm approximation of power spectra","author":"Gutknecht","year":"1986"},{"key":"10.1016\/0005-1098(91)90057-9_BIB22","series-title":"Proc. 1990 Amer. Control Conf.","article-title":"Identification in H\u221e: A robustly convergent, nonlinear algorithm","author":"Helmicki","year":"1990"},{"key":"10.1016\/0005-1098(91)90057-9_BIB23","series-title":"Proc. 1989 Amer. Control Conf.","article-title":"H\u221e identification of stable LSI systems: A scheme with direct application to control design","author":"Helmicki","year":"1989"},{"key":"10.1016\/0005-1098(91)90057-9_BIB24","volume":"Vol. XI","author":"Jackson","year":"1930"},{"key":"10.1016\/0005-1098(91)90057-9_BIB25","author":"Jenkins","year":"1969"},{"key":"10.1016\/0005-1098(91)90057-9_BIB26","author":"Katznelson","year":"1976"},{"key":"10.1016\/0005-1098(91)90057-9_BIB27","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1070\/RM1983v038n04ABEH004203","article-title":"Combinatorial foundations of information theory and the calculus of probabilities","volume":"38","author":"Kolmogorov","year":"1983","journal-title":"Russian Math. Sur."},{"key":"10.1016\/0005-1098(91)90057-9_BIB28","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1080\/00207177708922326","article-title":"Distributed parameter system identification","volume":"26","author":"Kubrusly","year":"1977","journal-title":"Int. J. Control"},{"key":"10.1016\/0005-1098(91)90057-9_BIB29","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1109\/TAC.1985.1103825","article-title":"Minimax frequency domain performance and robustness optimization of linear feedback systems","volume":"AC-30","author":"Kwakernaak","year":"1985","journal-title":"IEEE Trans. Aut. Control"},{"key":"10.1016\/0005-1098(91)90057-9_BIB30","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1016\/0005-1098(85)90042-1","article-title":"On the estimation of transfer functions","volume":"21","author":"Ljung","year":"1985","journal-title":"Automatica"},{"key":"10.1016\/0005-1098(91)90057-9_BIB31","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1093\/imamci\/1.4.323","article-title":"Black-box identification of transfer functions: Asymptotic results for increasing model order and data records","volume":"1","author":"Ljung","year":"1984","journal-title":"IMA J. Math. Control Inform."},{"key":"10.1016\/0005-1098(91)90057-9_BIB32","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/TAC.1985.1103995","article-title":"Asymptotic properties of black-box identification of transfer functions","volume":"AC-30","author":"Ljung","year":"1985","journal-title":"IEEE Trans. Aut. Control"},{"key":"10.1016\/0005-1098(91)90057-9_BIB33","author":"Lorentz","year":"1986"},{"key":"10.1016\/0005-1098(91)90057-9_BIB34","author":"Luyben","year":"1973"},{"key":"10.1016\/0005-1098(91)90057-9_BIB35","article-title":"On H\u221e identification of stable systems and optimal approximation","author":"M\u00e4kil\u00e4","year":"1989"},{"key":"10.1016\/0005-1098(91)90057-9_BIB36","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0005-1098(90)90127-4","article-title":"Approximation of stable systems by Laguerre filters","volume":"26","author":"M\u00e4kil\u00e4","year":"1990","journal-title":"Automatica"},{"key":"10.1016\/0005-1098(91)90057-9_BIB37","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1016\/0005-1098(90)90083-T","article-title":"Laguerre series approximation of infinite dimensional systems","volume":"26","author":"M\u00e4kil\u00e4","year":"1990","journal-title":"Automatica"},{"key":"10.1016\/0005-1098(91)90057-9_BIB38","author":"Partington","year":"1988"},{"key":"10.1016\/0005-1098(91)90057-9_BIB39","series-title":"Eigenvalues and s-numbers","author":"Pietsch","year":"1987"},{"key":"10.1016\/0005-1098(91)90057-9_BIB40","first-page":"45","article-title":"Parameter identification in distributed systems: A synthesizing overview","volume":"64","author":"Polis","year":"1976"},{"key":"10.1016\/0005-1098(91)90057-9_BIB41","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/0005-1098(80)90075-8","article-title":"Step response and frequency response methods","volume":"16","author":"Rake","year":"1980","journal-title":"Automatica"},{"key":"10.1016\/0005-1098(91)90057-9_BIB42","series-title":"Proc. IEEE Conf on Decision and Control","article-title":"Estimation of errors-in-variables models","author":"Rissanen","year":"1988"},{"key":"10.1016\/0005-1098(91)90057-9_BIB43","volume":"Vol. 23","author":"Szeg\u00f6","year":"1939"},{"key":"10.1016\/0005-1098(91)90057-9_BIB44","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF01398258","article-title":"Rational Chebyshev approximation on the unit disk","volume":"37","author":"Trefethen","year":"1981","journal-title":"Numer. Math."},{"key":"10.1016\/0005-1098(91)90057-9_BIB45","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0167-6911(89)90001-7","article-title":"Approximation and stabilization of distributed systems by lumbed systems","volume":"12","author":"Vidyasagar","year":"1989","journal-title":"Syst. Control Lett."},{"key":"10.1016\/0005-1098(91)90057-9_BIB46","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/00207178908559628","article-title":"Model reductions of high-order estimated models: The asymptotic ML approach","volume":"49","author":"Wahlberg","year":"1989","journal-title":"Int. J. Control"},{"key":"10.1016\/0005-1098(91)90057-9_BIB47","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0005-1098(87)90120-8","article-title":"From time series to linear system\u2014Part III. Approximate modeling","volume":"23","author":"Willems","year":"1987","journal-title":"Automatica"},{"key":"10.1016\/0005-1098(91)90057-9_BIB48","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/0024-3795(83)90073-3","article-title":"The singular-value decomposition of an infinite Hankel matrix","volume":"50","author":"Young","year":"1983","journal-title":"Linear Algebra Applic"},{"key":"10.1016\/0005-1098(91)90057-9_BIB49","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1109\/TAC.1979.1101976","article-title":"On the metric complexity of causal linear systems: \u03b5-entropy and \u03b5-dimension for continuous time","volume":"AC-24","author":"Zames","year":"1979","journal-title":"IEEE Trans. Aut. Control"},{"key":"10.1016\/0005-1098(91)90057-9_BIB50","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/TAC.1981.1102603","article-title":"Feedback and optimal sensitivity: model reference transformation, multiplicative seminorms, and approximative inverses","volume":"AC-26","author":"Zames","year":"1981","journal-title":"IEEE Trans. Aut. Control"}],"container-title":["Automatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0005109891900579?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0005109891900579?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,27]],"date-time":"2019-03-27T00:23:37Z","timestamp":1553646217000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0005109891900579"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,7]]},"references-count":51,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1991,7]]}},"alternative-id":["0005109891900579"],"URL":"https:\/\/doi.org\/10.1016\/0005-1098(91)90057-9","relation":{},"ISSN":["0005-1098"],"issn-type":[{"value":"0005-1098","type":"print"}],"subject":[],"published":{"date-parts":[[1991,7]]}}}