{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T14:32:41Z","timestamp":1742913161017,"version":"3.40.3"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319784571"},{"type":"electronic","value":"9783319784588"}],"license":[{"start":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T00:00:00Z","timestamp":1521763200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-319-78458-8_7","type":"book-chapter","created":{"date-parts":[[2018,3,22]],"date-time":"2018-03-22T02:40:29Z","timestamp":1521686429000},"page":"74-83","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Gr\u00fcnwald-Letnikov-Laguerre Modeling of\u00a0Discrete-Time Noncommensurate Fractional-Order State Space LTI MIMO Systems"],"prefix":"10.1007","author":[{"given":"Krzysztof J.","family":"Latawiec","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafa\u0142","family":"Stanis\u0142awski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marian","family":"\u0141ukaniszyn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marek","family":"Rydel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bogus\u0142aw R.","family":"Szkuta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,23]]},"reference":[{"key":"7_CR1","volume-title":"Fractional Differential Equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations. Academic Press, Orlando (1999)"},{"key":"7_CR2","series-title":"Series on Advances in Industrial Control","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-335-0","volume-title":"Fractional-order Systems and Controls: Fundamentals and Applications","author":"C Monje","year":"2010","unstructured":"Monje, C., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional-order Systems and Controls: Fundamentals and Applications. Series on Advances in Industrial Control. Springer, London (2010)"},{"key":"7_CR3","doi-asserted-by":"crossref","unstructured":"Chen, Y., Vinagre, B., Podlubny, I.: A new discretization method for fractional order differentiators via continued fraction expansion. In: Proceedings of DETC 2003, ASME Design Engineering Technical Conferences, Chicago, IL, vol. 340, pp. 349\u2013362 (2003)","DOI":"10.1115\/DETC2003\/VIB-48391"},{"issue":"6","key":"7_CR4","doi-asserted-by":"publisher","first-page":"1579","DOI":"10.1109\/TAC.2013.2244273","volume":"58","author":"G Maione","year":"2013","unstructured":"Maione, G.: On the Laguerre rational approximation to fractional discrete derivative and integral operators. IEEE Trans. Autom. Control 58(6), 1579\u20131585 (2013)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"7_CR5","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1090\/S0002-9947-2014-05887-X","volume":"367","author":"B Baeumer","year":"2015","unstructured":"Baeumer, B., Kovacs, M., Sankaranarayanan, H.: Higher order Gr\u00fcnwald approximations of fractional derivatives and fractional powers of operators. Trans. Am. Math. Soc. 367(2), 813\u2013834 (2015)","journal-title":"Trans. Am. Math. Soc."},{"issue":"1","key":"7_CR6","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1109\/JSEE.2012.00018","volume":"23","author":"Z Gao","year":"2012","unstructured":"Gao, Z.: Improved Oustaloup approximation of fractional-order operators using adaptive chaotic particle swarm optimization. J. Syst. Eng. Electron. 23(1), 145\u2013153 (2012)","journal-title":"J. Syst. Eng. Electron."},{"issue":"2","key":"7_CR7","doi-asserted-by":"publisher","first-page":"1387","DOI":"10.1007\/s11071-011-0075-6","volume":"67","author":"Z Gao","year":"2012","unstructured":"Gao, Z., Liao, X.: Rational approximation for fractional-order system by particle swarm optimization. Nonlinear Dyn. 67(2), 1387\u20131395 (2012)","journal-title":"Nonlinear Dyn."},{"key":"7_CR8","doi-asserted-by":"crossref","unstructured":"Khanra, M.: Rational approximation of fractional operator\u2014a comparative study. In: International Conference on Power, Control and Embedded Systems (ICPCES), Allahabad, India, pp. 1\u20135 (2010)","DOI":"10.1109\/ICPCES.2010.5698677"},{"key":"7_CR9","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.1016\/j.jcp.2007.02.001","volume":"225","author":"Y Lin","year":"2007","unstructured":"Lin, Y., Xu, C.: Finite difference\/spectral approximations for the time-fractional diffusion equation. J. Comput. Phys. 225, 1533\u20131552 (2007)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"7_CR10","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1023\/A:1006554907440","volume":"81","author":"Z Ditzian","year":"1998","unstructured":"Ditzian, Z.: Fractional derivatives and best approximation. Acta Mathematica Hungarica 81(4), 323\u2013348 (1998)","journal-title":"Acta Mathematica Hungarica"},{"issue":"10","key":"7_CR11","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1016\/j.sigpro.2006.02.004","volume":"86","author":"CC Tseng","year":"2006","unstructured":"Tseng, C.C.: Design of variable and adaptive fractional order FIR differentiators. Sig. Process. 86(10), 2554\u20132566 (2006)","journal-title":"Sig. Process."},{"issue":"4","key":"7_CR12","doi-asserted-by":"crossref","first-page":"907","DOI":"10.2478\/v10006-012-0067-9","volume":"22","author":"R Stanis\u0142awski","year":"2012","unstructured":"Stanis\u0142awski, R., Latawiec, K.J.: Normalized finite fractional differences - the computational and accuracy breakthroughs. Int. J. Appl. Math. Comput. Sci. 22(4), 907\u2013919 (2012)","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"7_CR13","doi-asserted-by":"crossref","unstructured":"Stanis\u0142awski, R., Latawiec, K.J.: Modeling of open-loop stable linear systems using a combination of a finite fractional derivative and orthonormal basis functions. In: Proceedings of the 15th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, pp. 411\u2013414 (2010)","DOI":"10.1109\/MMAR.2010.5587197"},{"key":"7_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2012\/732917","volume":"2012","author":"R Stanis\u0142awski","year":"2012","unstructured":"Stanis\u0142awski, R.: New Laguerre filter approximators to the Gr\u00fcnwald-Letnikov fractional difference. Math. Probl. Eng. 2012, 1\u201321 (2012). Article ID: 732917","journal-title":"Math. Probl. Eng."},{"key":"7_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2015\/512104","volume":"2015","author":"R Stanis\u0142awski","year":"2015","unstructured":"Stanis\u0142awski, R., Latawiec, K.J., \u0141ukaniszyn, M.: A comparative analysis of Laguerre-based approximators to the Gr\u00fcnwald-Letnikov fractional-order difference. Math. Probl. Eng. 2015, 1\u201310 (2015). Article ID: 512104","journal-title":"Math. Probl. Eng."},{"key":"7_CR16","doi-asserted-by":"crossref","unstructured":"Stanis\u0142awski, R., Latawiec, K.J., \u0141ukaniszyn, M., Ga\u0142ek, M.: Time-domain approximations to the Gr\u00fcnwald-Letnikov difference with application to modeling of fractional-order state space systems. In: 20th International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland, pp. 579\u2013584, August 2015","DOI":"10.1109\/MMAR.2015.7283939"},{"key":"7_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2016\/9590687","volume":"2016","author":"R Stanis\u0142awski","year":"2016","unstructured":"Stanis\u0142awski, R., Latawiec, K.J.: Fractional-order discrete-time Laguerre filters - a new tool for modeling and stability analysis of fractional-order LTI SISO systems. Discrete Dyn. Nature Soc. 2016, 1\u20139 (2016). Article ID: 9590687","journal-title":"Discrete Dyn. Nature Soc."},{"key":"7_CR18","doi-asserted-by":"publisher","unstructured":"Latawiec, K.J., Stanis\u0142awski, R., \u0141ukaniszyn, M., Rydel, M., Szkuta, B.R.: FFLD-based modeling of fractional-order state space LTI MIMO systems. In: International Conference on Applied Physics, System Science and Computers (APSAC2016). Lecture Notes in Electrical Engineering, vol. 428. Springer (2017). https:\/\/doi.org\/10.1007\/978-3-319-53934-8_36","DOI":"10.1007\/978-3-319-53934-8_36"},{"issue":"2","key":"7_CR19","first-page":"353","volume":"61","author":"R Stanis\u0142awski","year":"2013","unstructured":"Stanis\u0142awski, R., Latawiec, K.J.: Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: new necessary and sufficient conditions for asymptotic stability. Bull. Polish Acad. Sci. Tech. Sci. 61(2), 353\u2013361 (2013)","journal-title":"Bull. Polish Acad. Sci. Tech. Sci."},{"issue":"2","key":"7_CR20","first-page":"362","volume":"61","author":"R Stanis\u0142awski","year":"2013","unstructured":"Stanis\u0142awski, R., Latawiec, K.J.: Stability analysis for discrete-time fractional-order LTI state-space systems. Part II: new stability criterion for FD-based systems. Bull. Polish Acad. Sci. Tech. Sci. 61(2), 362\u2013370 (2013)","journal-title":"Bull. Polish Acad. Sci. Tech. Sci."}],"container-title":["Lecture Notes in Electrical Engineering","Non-Integer Order Calculus and its Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-78458-8_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T22:48:59Z","timestamp":1604011739000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-78458-8_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,23]]},"ISBN":["9783319784571","9783319784588"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-78458-8_7","relation":{},"ISSN":["1876-1100","1876-1119"],"issn-type":[{"type":"print","value":"1876-1100"},{"type":"electronic","value":"1876-1119"}],"subject":[],"published":{"date-parts":[[2018,3,23]]},"assertion":[{"value":"23 March 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}