{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T23:21:54Z","timestamp":1742944914910,"version":"3.40.3"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319230382"},{"type":"electronic","value":"9783319230399"}],"license":[{"start":{"date-parts":[[2015,8,2]],"date-time":"2015-08-02T00:00:00Z","timestamp":1438473600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,8,2]],"date-time":"2015-08-02T00:00:00Z","timestamp":1438473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-23039-9_8","type":"book-chapter","created":{"date-parts":[[2015,8,1]],"date-time":"2015-08-01T08:31:17Z","timestamp":1438417877000},"page":"93-103","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Stability Properties of Discrete Time-Domain Oustaloup Approximation"],"prefix":"10.1007","author":[{"given":"Jerzy","family":"Baranowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Waldemar","family":"Bauer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marta","family":"Zag\u00f3rowska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,8,2]]},"reference":[{"key":"8_CR1","first-page":"171","volume-title":"Lecture Notes in Electrical Engineering","author":"Piotr Bania","year":"2013","unstructured":"Bania, P., Baranowski, J.: Laguerre polynomial approximation of fractional order linear systems. In Mitkowski, W., Kacprzyk, J., Baranowski, J. (eds.) Advances in the Theory and Applications of Non-integer Order Systems: 5th Conference on Non-integer Order Calculus and Its Applications, Cracow, Poland, pp. 171\u2013182. Springer, Berlin (2013)"},{"key":"8_CR2","doi-asserted-by":"crossref","unstructured":"Baranowski, J., Bauer, W., Zagorowska, M., Dziwinski, T., Piatek P.: Time-domain oustaloup approximation. In: 20th International Conference On. IEEE Methods and Models in Automation and Robotics (MMAR), (2015) (in printing)","DOI":"10.1109\/MMAR.2015.7283857"},{"key":"8_CR3","doi-asserted-by":"crossref","unstructured":"Baranowski, J., Pi\u0105tek, P., Bauer, W., Dziwi\u0144ski, T., Zag\u00f3rowska, M.: Bi-fractional filters, part 2: Right half-plane case. In: 19th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 369\u2013373 (2014)","DOI":"10.1109\/MMAR.2014.6957381"},{"key":"8_CR4","doi-asserted-by":"crossref","unstructured":"Baranowski, J., Zag\u00f3rowska, M., Bania, P., Bauer, W., Dziwi\u0144ski, T., Pi\u0105tek, P.: Impulse response approximation method for bi-fractional filter. In: 19th IEEE International Conference On Methods and Models in Automation and Robotics (MMAR), pp. 379\u2013383 (2014)","DOI":"10.1109\/MMAR.2014.6957383"},{"key":"8_CR5","unstructured":"Bauer, W., Baranowski, J., Dziwinski, T., Piatek, P., Zagorowska, M.: Stabilisation of magnetic levitation with a pi$$^{\\lambda }$$d$$^{\\mu }$$ controller. In: 20th IEEE International Conference On Methods and Models in Automation and Robotics (MMAR), (2015) (in printing)"},{"key":"8_CR6","unstructured":"Bauer, W., Baranowski, J., Mitkowski, W.: Non-integer order PI$$^\\alpha $$D$$^\\mu $$ control ICU-MM. In: Mitkowski, W., Kacprzyk, J., Baranowski, J. (eds.) Advances in the Theory and Applications of Non-integer Order Systems: 5th Conference on Non-integer Order Calculus and Its Applications, Cracow, Poland, pp. 171\u2013182. Springer, Berlin (2013)"},{"key":"8_CR7","doi-asserted-by":"crossref","unstructured":"Bauer, W., Dziwi\u0144ski, T., Baranowski, J., Pi\u0105tek, P., Zag\u00f3rowska, M.: Comparison of performance indices for tuning of pi$$^{\\lambda }$$d$$^{\\mu }$$ controller for magnetic levitation system. In Latawiec, K.J., \u0141ukaniszyn, M., Stanis\u0142awski, R. (eds.) Advances in Modelling and Control of Noninteger-order Systems\u20146th Conference on Non-Integer Orfer Caculus and its Applications. Springer, Berlin (2014)","DOI":"10.1007\/978-3-319-09900-2_12"},{"key":"8_CR8","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14574-2","volume-title":"The analysis of fractional differential equations: an application-oriented exposition using differential operators of caputo type","author":"K Diethelm","year":"2010","unstructured":"Diethelm, K.: The analysis of fractional differential equations: an application-oriented exposition using differential operators of caputo type. Lecture Notes in Mathematics. Springer, Berlin (2010)"},{"key":"8_CR9","doi-asserted-by":"crossref","unstructured":"Dziwi\u0144ski, T., Bauer, W., Baranowski, J., Pi\u0105tek, P., Zagorowska, M.: Robust non-integer order controller for air heater. In: 19th IEEE International Conference On Methods and Models in Automation and Robotics (MMAR), pp. 434\u2013438 (2014)","DOI":"10.1109\/MMAR.2014.6957393"},{"key":"8_CR10","doi-asserted-by":"crossref","unstructured":"Dziwi\u0144ski, T., Bauer, W., Baranowski, J., Pi\u0105tek, P., Zag\u00f3rowska, M.: Robust non-integer order controller for air heating process trainer. In: Latawiec, K.J., \u0141ukaniszyn, M., Stanis\u0142awski, R. (eds.) Advances in Modelling and Control of Noninteger-order Systems\u20146th Conference on Non-Integer Orfer Caculus and its Applications. Springer, Berlin (2014)","DOI":"10.1007\/978-3-319-09900-2_23"},{"key":"8_CR11","doi-asserted-by":"crossref","unstructured":"Dziwinski, T., Piatek, P., Baranowski, J., Bauer, W., Zagorowska, M.: On the practical implementation of non-integer order filters. In: 20th IEEE International Conference On Methods and Models in Automation and Robotics (MMAR), (2015) (in printing)","DOI":"10.1109\/MMAR.2015.7284000"},{"key":"8_CR12","doi-asserted-by":"crossref","unstructured":"Hairer, E., Wanner, G.: Solving ordinary differential equations: II stiff and differential-algebraic problems, 1 edn. Springer, Berlin (1991)","DOI":"10.1007\/978-3-662-09947-6_1"},{"key":"8_CR13","series-title":"Lecture Notes in Control and Information Sciences","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20502-6","volume-title":"Selected problems of fractional systems theory","author":"T Kaczorek","year":"2011","unstructured":"Kaczorek, T.: Selected problems of fractional systems theory. Lecture Notes in Control and Information Sciences. Springer, Berlin (2011)"},{"key":"8_CR14","doi-asserted-by":"crossref","unstructured":"Kawala-Janik, A., Podpora, M., Baranowski, J., Bauer, W., Pelc, M.: Innovative approach in analysis of eeg and emg signals ? comparision of the two novel methods. In: 19th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 804\u2013807 (2014)","DOI":"10.1109\/MMAR.2014.6957459"},{"issue":"10","key":"8_CR15","doi-asserted-by":"publisher","first-page":"2203","DOI":"10.1080\/00207721.2013.766773","volume":"45","author":"S Liang","year":"2014","unstructured":"Liang, S., Peng, C., Liao, Z., Wang, Y.: State space approximation for general fractional order dynamic systems. Int. J. Syst. Sci. 45(10), 2203\u20132212 (2014)","journal-title":"Int. J. Syst. Sci."},{"key":"8_CR16","volume-title":"Digital control and estimation: a unified approach","author":"RH Middleton","year":"1990","unstructured":"Middleton, R.H., Goodwin, G.C.: Digital control and estimation: a unified approach. Prentice-Hall International, Englewood Cliffs (1990)"},{"key":"8_CR17","series-title":"Advances in Industrial Control","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84996-335-0","volume-title":"Fractional-order Systems and Controls","author":"Concepci\u00f3n A. Monje","year":"2010","unstructured":"Monje, C.A., Chen, Y., Vinagre, B.M., Xue, D., Feliu, V.: Fractional-order systems and controls. Fundamentals and applications. Advances in Industrial Control. Springer, London (2010)"},{"issue":"1","key":"8_CR18","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1109\/81.817385","volume":"47","author":"A Oustaloup","year":"2000","unstructured":"Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circ. Syst. I: Fundam. Theory Appl. 47(1), 25\u201339 (2000)","journal-title":"IEEE Trans. Circ. Syst. I: Fundam. Theory Appl."},{"key":"8_CR19","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/978-3-642-18101-6_6","volume-title":"Fractional-Order Nonlinear Systems","author":"Ivo Petr\u00e1\u0161","year":"2011","unstructured":"Petr\u00e1\u0161, I.: Fractional-order nonlinear systems. Modeling, Analysis and Simulation. Nonlinear Physical Science. Springer, Berlin (2011)"},{"issue":"2","key":"8_CR20","first-page":"101","volume":"5","author":"P Pi\u0105tek","year":"2011","unstructured":"Pi\u0105tek, P., Baranowski, J.: Investigation of fixed-point computation influence on numerical solutions of fractional differential equations. Acta Mech. et Automatica 5(2), 101\u2013107 (2011)","journal-title":"Acta Mech. et Automatica"},{"key":"8_CR21","doi-asserted-by":"crossref","unstructured":"Pi\u0105tek, P., Zag\u00f3rowska, M., Baranowski, J., Bauer, W., Dziwi\u0144ski, T.: Discretisation of different non-integer order system approximations. In: 19th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 429\u2013433 (2014)","DOI":"10.1109\/MMAR.2014.6957392"},{"key":"8_CR22","unstructured":"Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Mathematics in Science and Engineering. Elsevier Science, Amsterdam (1999)"},{"issue":"5","key":"8_CR23","doi-asserted-by":"publisher","first-page":"1644","DOI":"10.1016\/j.camwa.2009.08.006","volume":"59","author":"C Tricaud","year":"2010","unstructured":"Tricaud, C., Chen, Y.: An approximate method for numerically solving fractional order optimal control problems of general form. Comput. Math. Appl. 59(5), 1644\u20131655 (2010). Fractional Differentiation and Its Applications","journal-title":"Comput. Math. Appl."},{"issue":"10","key":"8_CR24","doi-asserted-by":"publisher","first-page":"3117","DOI":"10.1016\/j.camwa.2012.03.099","volume":"64","author":"J Trigeassou","year":"2012","unstructured":"Trigeassou, J., Maamri, N., Sabatier, J., Oustaloup, A.: State variables and transients of fractional order differential systems. Comput. Math. Appl. 64(10), 3117\u20133140 (2012). Advances in FDE, III","journal-title":"Comput. Math. Appl."},{"key":"8_CR25","doi-asserted-by":"crossref","unstructured":"Zag\u00f3rowska, M., Baranowski, J., Bania, P., Pi\u0105tek, P., Bauer, W., Dziwi\u0144ski, W.: Impulse response approximation method for \u201cfractional order lag\u201d. In: Latawiec, K.J., \u0141ukaniszyn, M., Stanis\u0142awski, R. (eds.) Advances in Modelling and Control of Noninteger-Order Systems\u20146th Conference on Non-Integer Orfer Caculus and its Applications. Springer, Berlin (2014)","DOI":"10.1007\/978-3-319-09900-2_11"},{"key":"8_CR26","unstructured":"Zagorowska, M., Baranowski, J., Bauer, W., Dziwinski, T., Piatek, P.: Parametric optimization of pd controller using laguerre approximation. In: 20th IEEE International Conference On Methods and Models in Automation and Robotics (MMAR), (2015) (in printing)"},{"key":"8_CR27","doi-asserted-by":"crossref","unstructured":"Zag\u00f3rowska, M., Baranowski, J., Bauer, W., Dziwi\u0144ski, T., Pi\u0105tek, P.: Simulational analysis of non-integer order system behaviour under relay control. In: 19th IEEE International Conference On Methods and Models in Automation and Robotics (MMAR), pp. 374\u2013378 (2014)","DOI":"10.1109\/MMAR.2014.6957382"}],"container-title":["Lecture Notes in Electrical Engineering","Theoretical Developments and Applications of Non-Integer Order Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-23039-9_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T07:41:50Z","timestamp":1676965310000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-23039-9_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,2]]},"ISBN":["9783319230382","9783319230399"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-23039-9_8","relation":{},"ISSN":["1876-1100","1876-1119"],"issn-type":[{"type":"print","value":"1876-1100"},{"type":"electronic","value":"1876-1119"}],"subject":[],"published":{"date-parts":[[2015,8,2]]},"assertion":[{"value":"2 August 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}