Stability of linear continuous-time fractional order systems with delays of the retarded type

• Autorzy: Busłowicz M.
• Języki publikacji: EN

Abstrakty

EN

New frequency domain methods for stability analysis of linear continuous-time fractional order systems with delays of the retarded type are given. The methods are obtained by generalisation to the class of fractional order systems with delays of the Mikhailov stability criterion and the modified Mikhailov stability criterion known from the theory of natural order systems without and with delays. The study is illustrated by numerical examples of time-delay systems of commensurate and non-commensurate fractional orders.

Słowa kluczowe

EN

fractional system; linear; continuous-time; stability; delays; retarded type

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2008
• Tom: Vol. 56, nr 4
• Strony: 319--317
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Busłowicz M.

• Faculty of Electrical Engineering, Białystok Technical University, 45D Wiejska St., 15-351 Białystok, Poland

Bibliografia

• [1] S. Das, Functional Fractional Calculus for System Identification and Controls, Springer, Berlin, 2008.
• [2] T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18 (2), 223–228 (2008).
• [3] M.D. Ortigueira, “Introduction to fractional linear systems. Part 1: Continuous-time case”, IEE Proc. – Vis. Image Signal Process 147, 62–70 (2000).
• [4] M.D. Ortigueira, “Introduction to fractional linear systems. Part 2: Discrete-time systems”, IEE Proc. – Vis. Image Signal Process 147, 71–78 (2000).
• [5] P. Ostalczyk, Epitome of the Fractional Calculus, Theory and its Applications in Automatics, Publishing Department of Technical University of Łódz, Łódz, 2008, (in Polish).
• [6] J. Sabatier, O.P. Agrawal, and J.A.T. Machado, Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering, Springer, London, 2007.
• [7] D. Sierociuk, Estimation and Control of Discrete Dynamical Systems of Fractional Order in State Space, PhD Dissertation, Faculty of Electrical Engineering, Warsaw University of Technology, Warszawa, 2007, (in Polish).
• [8] D. Valerio and J. Sa da Costa, “Tuning of fractional PID controllers with Ziegler-Nichols-type rules”, Signal Processing 86, 2771–2784 (2006).
• [9] B.M. Vinagre, C.A. Monje, and A.J. Calderon, “Fractional order systems and fractional order control actions”, Lecture 3 of IEEE CDC’02: Fractional Calculus Applications in Automatic Control and Robotics 2, CD-ROM (2002).
• [10] M. Busłowicz, “Stability of linear continuous-time fractional systems of commensurate order”, Measurements Automatics Robotics 2, 475–484 (2008), (in Polish).
• [11] M. Busłowicz, “Frequency domain method for stability analysis of linear continuous-time fractional systems”, in: K. Malinowski and L. Rutkowski (eds.), Recent Advances in Control and Automation, pp. 83–92, Academic Publishing House EXIT, Warsaw, 2008.
• [12] K. Gałkowski, O. Bachelier, and A. Kummert, “Fractional polynomial and nD systems a continuous case”, Proc. IEEE Conference on Decision & Control, CD-ROM (2006).
• [13] D. Matignon, “Stability results on fractional differential equation with applications to control processing”, Proc. IMACS, Lille, CD-ROM (1996).
• [14] D. Matignon, “Stability properties for generalized fractional differential systems”, Proc. ESAIM, 145–158 (1998).
• [15] R. Bellman and C.S. Cooke, Differential-Difference Equations, Academic Press, New York, 1963.
• [16] M. Busłowicz, Robust Stability of Dynamical Linear Stationary Systems with Delays, Publishing Department of Technical University of Białystok, Warszawa-Białystok, 2000, (in Polish).
• [17] H. Górecki, Analysis and Synthesis of Control Systems with Delay, WNT, Warszawa, 1971, (in Polish).
• [18] H. Górecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time Delay Systems, PWN-J.Wiley, Warszawa-Chichester, 1989.
• [19] H. Górecki and A. Korytowski, Advances in Optimization and Stability Analysis of Dynamical Systems, Publishing Department of University of Mining and Metallurgy, Kraków, 1993.
• [20] C. Bonnet and J.R. Partington, “Coprime factorizations and stability of fractional differential systems”, Systems and Control Letters 41, 167–174 (2000).
• [21] C. Bonnet and J. R. Partington, “Analysis of fractional delay systems of retarded and neutral type”, Automatica 38, 1133–1138 (2002).
• [22] C. Bonnet and J.R. Partington, “Stabilization of some fractional delay systems of neutral type”, Automatica 43, 2047–2053 (2007).
• [23] C. Hwang and Y-Q. Cheng, “A numerical method for stability testing of fractional delay systems”, Automatica 42, 825–831 (2006).
• [24] N. Ozturk and A. Uraz, “An analysis stability test for a certain class of distributed parameter systems with delays”, IEEE Trans. Circuits and Systems 32, 393–396 (1985).
• [25] M. Busłowicz, Stability of Linear Time-Invariant Systems with Uncertain Parameters, Publishing Department of Technical University of Białystok, Białystok, 1997, (in Polish).
• [26] T. Kaczorek, Theory of Control Systems, WNT, Warszawa, 1974, (in Polish).
• [27] W.C. Wright and T.W. Kerlin, “An efficient computer oriented method for stability analysis of large multivariable systems”, Trans. ASME J. Basic Eng. 92, 279–286 (1970).