Open Access

Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold


Cite

Aström, K.J., Hagander, P. and Sternby, J. (1984). Zeros of sampled systems, Automatica 20(1): 31-38.10.1016/0005-1098(84)90062-1Search in Google Scholar

Bàrcena, R., de la Sen, M. and Sagastabeitia, I. (2000). Improving the stability properties of the zeros of sampled systems with fractional order hold, IEE Proceedings: Control Theory and Applications 147(4): 456-464.10.1049/ip-cta:20000550Search in Google Scholar

Bàrcena, R., de la Sen, M., Sagastabeitia, I. and Collantes, J.M. (2001). Discrete control for a computer hard disk by using a fractional order hold device, IEE Proceedings: Control Theory and Applications 148(2): 117-124.10.1049/ip-cta:20010196Search in Google Scholar

Błachuta, M.J. (1998). On zeros of pulse transfer functions of systems with first-order hold, Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, USA, Vol. 1, pp. 307-312.Search in Google Scholar

Błachuta, M.J. (1999). On zeros of pulse transfer functions, IEEE Transactions on Automatic Control 44(6): 1229-1234.10.1109/9.769380Search in Google Scholar

Błachuta, M.J. (2001). On fast sampling zeros of systems with fractional-order hold, Proceedings of the 2001 American Control Conference, Arlington, VA, USA, Vol. 4, pp. 3229-3230.Search in Google Scholar

Chan, J.T. (1998). On the stabilization of discrete system zeros, International Journal of Control 69(6): 789-796.10.1080/002071798222541Search in Google Scholar

Chan, J.T. (2002). Stabilization of discrete system zeros: An improved design, International Journal of Control 75(10): 759-765.10.1080/00207170210144920Search in Google Scholar

Feuer, A. and Goodwin, G. (1996). Sampling in Digital Signal Processing and Control, Birkhauser, Boston, MA.10.1007/978-1-4612-2460-0Search in Google Scholar

Filatov, N.M., Keuchel, U. and Unbehauen, H. (1996). Dual control for an unstable mechanical plant, IEEE Control Systems Magazine 16(4): 31-37.10.1109/37.526913Search in Google Scholar

Hagiwara, T. (1996). Analytic study on the intrinsic zeros of sampled-data system, IEEE Transactions on Automatic Control 41(2): 261-263.10.1109/9.481531Search in Google Scholar

Hagiwara, T., Yuasa, T. and Araki, M. (1992). Limiting properties of the zeros of sampled-data systems with zeroand first-order holds, Proceeding of the 31st Conference on Decision and Control, Tucson, AZ, USA, pp. 1949-1954.Search in Google Scholar

Hagiwara, T., Yuasa, T. and Araki, M. (1993). Stability of the limiting zeros of sampled-data systems with zeroand first-order holds, International Journal of Control 58(6): 1325-1346.10.1080/00207179308923057Search in Google Scholar

Hayakawa, Y., Hosoe, S. and Ito, M. (1983). On the limiting zeros of sampled multivariable systems, Systems and Control Letters 2(5): 292-300.10.1016/S0167-6911(83)80006-1Search in Google Scholar

Ishitobi, M. (1996). Stability of zeros of sampled system with fractional order hold, IEE Proceedings: Control Theory and Applications 143(2): 296-300.10.1049/ip-cta:19960394Search in Google Scholar

Ishitobi, M. (2000). A stability condition of zeros of sampled multivariable systems, IEEE Transactions on Automatic Control AC-45(2): 295-299.10.1109/9.839952Search in Google Scholar

Ishitobi, M., Nishi, M. and Kunimatsu, S. (2013). Asymptotic properties and stability criteria of zeros of sampled-data models for decouplable MIMO systems, IEEE Transactions on Automatic Control 58(11): 2985-2990.10.1109/TAC.2013.2261175Search in Google Scholar

Isidori, A. (1995). Nonlinear Control Systems: An Introduction, Springer Verlag, New York, NY.10.1007/978-1-84628-615-5Search in Google Scholar

Kabamba, P.T. (1987). Control of linear systems using generalized sampled-data hold functions, IEEE Transactions on Automatic Control AC-32(7): 772-783.10.1109/TAC.1987.1104711Search in Google Scholar

Kaczorek, T. (1987). Stability of periodically switched linear systems and the switching frequency, International Journal of System Science 18(4): 697-726.10.1080/00207728708964001Search in Google Scholar

Kaczorek, T. (2010). Decoupling zeros of positive discrete-time linear systems, Circuits and Systems 1: 41-48.10.4236/cs.2010.12007Search in Google Scholar

Kaczorek, T. (2013). Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(1): 29-33, DOI: 10.2478/amcs-2013-0003.10.2478/amcs-2013-0003Search in Google Scholar

Karampetakis, N.P. and Karamichalis, R. (2014). Discretization of singular systems and error estimation, International Journal of Applied Mathematics and Computer Science 24(1): 65-73, DOI: 10.2478/amcs-2014-0005.10.2478/amcs-2014-0005Search in Google Scholar

Khalil, H. (2002). Nonlinear Systems, Prentice-Hall, London.Search in Google Scholar

Liang, S. and Ishitobi, M. (2004a). Properties of zeros of discretised system using multirate input and hold, IEE Proceedings: Control Theory and Applications 151(2): 180-184.10.1049/ip-cta:20040038Search in Google Scholar

Liang, S. and Ishitobi, M. (2004b). The stability properties of the zeros of sampled models for time delay systems in fractional order hold case, Dynamics of Continuous, Discrete and Impulsive Systems, B: Applications and Algorithms 11(3): 299-312.Search in Google Scholar

Liang, S., Ishitobi, M., Shi,W. and Xian, X. (2007). On stability of the limiting zeros of discrete-time MIMO systems, ACTA Automatica SINICA 33(4): 439-441, (in Chinese).Search in Google Scholar

Liang, S., Ishitobi, M. and Zhu, Q. (2003). Improvement of stability of zeros in discrete-time multivariable systems using fractional-order hold, International Journal of Control 76(17): 1699-1711.10.1080/00207170310001631945Search in Google Scholar

Liang, S., Xian, X., Ishitobi, M. and Xie, K. (2010). Stability of zeros of discrete-time multivariable systems with GSHF, International Journal of Innovative Computing, Information and Control 6(7): 2917-2926.Search in Google Scholar

Middleton, R. and Freudenberg, J. (1995). Non-pathological sampling for generalized sampled-data hold functions, Automatica 31(2): 315-319.10.1016/0005-1098(94)00095-ZSearch in Google Scholar

Ostalczyk, P. (2012). Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains, International Journal of Applied Mathematics and Computer Science 22(3): 533-538, DOI: 10.2478/v10006-012-0040-7.10.2478/v10006-012-0040-7Search in Google Scholar

Passino, K.M. and Antsaklis, P.J. (1988). Inverse stable sampled low-pass systems, International Journal of Control 47(6): 1905-1913.10.1080/00207178808906145Search in Google Scholar

Ruzbehani, M. (2010). A new tracking controller for discrete-time SISO non minimum phase systems, Asian Journal of Control 12(1): 89-95.10.1002/asjc.163Search in Google Scholar

Tokarzewski, J. (2009). Zeros of Linear Systems, Springer, Berlin.Search in Google Scholar

Ugalde, U., Bàrcena, R. and Basterretxea, K. (2012). Generalized sampled-data hold functions with asymptotic zero-order hold behavior and polynomic reconstruction, Automatica 48(6): 1171-1176.10.1016/j.automatica.2012.03.004Search in Google Scholar

Weller, S.R. (1999). Limiting zeros of decouplable MIMO systems, IEEE Transactions on Automatic Control 44(1): 292-300.10.1109/9.739097Search in Google Scholar

Weller, S.R., Moran, W., Ninness, B. and Pollington, A.D. (2001). Sampling zeros and the Euler-Frobenius polynomials, IEEE Transactions on Automatic Control 46(2): 340-343.10.1109/9.905706Search in Google Scholar

Yuz, J.I., Goodwin, G.C. and Garnier, H. (2004). Generalized hold functions for fast sampling rates, 43rd IEEE Conference on Decision and Control (CDC’2004), Atlantis, The Bahamas, Vol. 46, pp. 761-765.Search in Google Scholar

Zeng, C., Liang, S., Li, H. and Su, Y. (2013). Current development and future challenges for zero dynamics of discrete-time systems, Control Theory & Applications 30(10): 1213-1230, (in Chinese).Search in Google Scholar

Zhang, Y., Kostyukova, O. and Chong, K.T. (2011). A new time-discretization for delay multiple-input nonlinear systems using the Taylor method and first order hold, Discrete Applied Mathematics 159(9): 924-938. 10.1016/j.dam.2011.01.022Search in Google Scholar

eISSN:
2083-8492
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics