Bonnet, C.; Partington, J. R. Coprime factorizations and stability of fractional differential systems. (English) Zbl 0985.93048 Syst. Control Lett. 41, No. 3, 167-174 (2000). Summary: We give a frequency-domain approach to stabilization for a large class of systems with transfer functions involving fractional powers of \(s.\) A necessary and sufficient criterion for BIBO stability is given, and it is shown how to construct coprime factorizations and associated Bézout factors in order to parametrize all stabilizing controllers of these systems. Cited in 60 Documents MSC: 93D15 Stabilization of systems by feedback 93C80 Frequency-response methods in control theory 93D25 Input-output approaches in control theory Keywords:fractional system; BIBO stability; coprime factorization; Bézout identity; Youla parametrization; heat equation; transmission line; stabilizing controllers; frequency domain stabilization PDFBibTeX XMLCite \textit{C. Bonnet} and \textit{J. R. Partington}, Syst. Control Lett. 41, No. 3, 167--174 (2000; Zbl 0985.93048) Full Text: DOI References: [1] Bonnet, C.; Partington, J. R., Bézout factors and \(L^1\)-optimal controllers for delay systems using a two-parameter compensator scheme, IEEE Trans. Automat. Control, 44, 1512-1521 (1999) · Zbl 0959.93052 [2] Curtain, R. F.; Zwart, H. J., An Introduction to Infinite Dimensional Linear Systems Theory (1995), Springer: Springer Berlin · Zbl 0646.93014 [3] Curtain, R. F., A synthesis of time and frequency domain methods for the control of infinite-dimensional systems: a system theoretic approach, (Banks, H. T., Control and Estimation in Distributed Parameter Systems, SIAM, Philadelphia (1992)), 171-224 [4] Glover, K.; Lam, J.; Partington, J. R., Rational approximation of a class of infinite-dimensional systems I: singular values of Hankel operators, Math. Control Signal Systems, 3, 325-344 (1990) · Zbl 0727.41020 [5] Glover, K.; Lam, J.; Partington, J. R., Rational approximation of a class of infinite-dimensional systems II: optimal convergence rates of \(L_∞\) approximants, Math. Control Signal Systems, 4, 233-246 (1991) · Zbl 0733.41023 [6] Gripenberg, G.; Londen, S. O.; Staffans, O., Volterra Integral and Functional Equations (1990), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0695.45002 [7] J.-J. Loiseau, H. Mounier, Stabilisation de l’équation de la chaleur commandée en flux, in: Systèmes Différentiels Fractionnaires, Modèles, Méthodes et Applications, Vol. 5, ESAIM Proceedings, SMAI, Paris 1998, pp. 131-144.; J.-J. Loiseau, H. Mounier, Stabilisation de l’équation de la chaleur commandée en flux, in: Systèmes Différentiels Fractionnaires, Modèles, Méthodes et Applications, Vol. 5, ESAIM Proceedings, SMAI, Paris 1998, pp. 131-144. · Zbl 0913.73052 [8] Mäkilä, P. M.; Partington, J. R., Robust stabilization - BIBO stability, distance notions and robustness optimization, Automatica, 29, 681-693 (1993) · Zbl 0771.93068 [9] D. Matignon, Stability properties for generalized fractional differential systems, in: Systèmes Différentiels Fractionnaires, Modèles, Méthodes et Applications, Vol. 5, ESAIM Proceedings, SMAI, Paris 1998, pp. 145-158.; D. Matignon, Stability properties for generalized fractional differential systems, in: Systèmes Différentiels Fractionnaires, Modèles, Méthodes et Applications, Vol. 5, ESAIM Proceedings, SMAI, Paris 1998, pp. 145-158. · Zbl 0920.34010 [10] Miller, K. S.; Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley: Wiley New York · Zbl 0789.26002 [11] G. Montseny, Diffusive representation of pseudo-differential time-operators, in: Systèmes Différentiels Fractionnaires, Modèles, Méthodes et Applications, Vol. 5, ESAIM Proceedings, SMAI, Paris 1998, pp. 159-175.; G. Montseny, Diffusive representation of pseudo-differential time-operators, in: Systèmes Différentiels Fractionnaires, Modèles, Méthodes et Applications, Vol. 5, ESAIM Proceedings, SMAI, Paris 1998, pp. 159-175. · Zbl 0916.93022 [12] Weber, E., Linear Transient Analysis, Vol. II (1956), Wiley: Wiley New York This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.