Stabilization of fractional positive continuous-time linear systems with delays in sectors of left half complex plane by state-feedbacks

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

The problem of stabilization of fractional positive linear continuous-time linear systems with delays by state-feedbacks is addressed. The gain matrix of the state feedback is chosen so that the zeros of the closed-loop polynomial are located in a sector of the left half of complex plane. Necessary and sufficient conditions for the solvability of the problem are established and a procedure for computation of a gain matrix of the feedback is proposed. The considerations are illustrated by a numerical example.

Słowa kluczowe

EN

fractional; positive; continuous-time; linear; system; state-feedback; stabilization

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2010
• Tom: Vol. 39, no 3
• Strony: 783--795
• Opis fizyczny: Bibliogr. 27 poz., wykr.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• BUSLOWICZ, M. (2008a) Stability of linear continuous-time fractional order systems with delays of the retarded type. Bull. Pol. Acad. Sci. Techn., 56 (4), 319-324.
• BUSLOWICZ, M. (2008b) Frequency domain method for stability analysis of linear continuous-time fractional systems. In: K. Malinowski, L. Rutkowski, eds., Recent Advances in Control and Automation. Acad. Publ. House EXIT, Warsaw, 83-92.
• FARINA, L. and RINALDI, S. (2000) Positive Linear Systems; Theory and Applications. J. Wiley, New York.
• GALKOWSKI, K. and KUMMERT, A. (2005) Fractional polynomials and nD systems. Proc IEEE Int. Symp. Circuits and Systems, ISCAS’2005, Kobe, Japan, CD-ROM.
• KACZOREK, T. (2002) Positive ID and 2D Systems. Springer-Verlag, London.
• KACZOREK, T. (2007) Reachability and controllability to zero of positive fractional discrete-time systems. Machine Intelligence and Robotic Control, 6 (4) (2004), 139-143.
• KACZOREK, T. (2008a) Asymptotic stability of positive ID and 2D linear systems. In: K. Malinowski, L. Rutkowski, eds., Recent Advances in Control and Automation. Acad. Publ. House EXIT, Warsaw, 41-52.
• KACZOREK, T. (2008b) Practical stability of positive fractional discrete-time systems. Bull. Pol. Acad. Sci. Techn., 56 (4), 313-318.
• KACZOREK, T. (2008c) Fractional positive continuous-time linear systems and their reachability. Int. J. Appl. Math. Comput. Sci., 18 (2), 223-228.
• KACZOREK, T. (2009a) Stabilization of fractional discrete-time linear systems using state-feedback. Proc. Conf. LOGITRANS, April 15-17, Szczyrk 2009.
• KACZOREK, T. (2009b) Stability of positive continuous-time linear systems with delays. Bull. Pol. Acad. Sci. Techn., 57 (4), 395-398.
• KACZOREK, T. (2009c) Positivity and stabilization of 2D linear systems with delays. Proc. MMAR Conference 2009, Szczecin (CD-ROM).
• NISHIMOTO, K. (1984) Fractional Calculus. Descartes Press, Koriama.
• OLDHAM, K.B. and SPANIER, J. (1974) The Fractional Calculus. Academic Press, New York.
• ORTIGUEIRA, M.D. (1997) Fractional discrete-time linear systems. Proc. of the IEE-ICASSP 97, Munich, Germany. IEEE, New York, 3, 2241-2244.
• OSTALCZYK, P. (2000) The non-integer difference of the discrete-time function and its application to the control system synthesis. Int. J. Syst. Sci., 31 (12), 1551-1561.
• OSTALCZYK, P. (2004a) Fractional-Order Backward Difference Equivalent Forms Part I – Homer’s Form. Proc. 1st IFAC Workshop on Fractional Differentiation and its Applications, FDA '04, Bordeaux, France, 342-347.
• OSTALCZYK, P. (2004b) Fractional-Order Backward Difference Equivalent Forms Part II - Polynomial Form. Proc. 1st IFAC Workshop on Frac-tional Differentiation and its Applications, FDA ‘04, Bordeaux, France, 348-353.
• OSTALCZYK, P. (2008) Epitome of the Fractional Calculus. Technical University of Lodz Publishing House, Lodz (in Polish).
• OUSTALOUP, A. (1993) Commande CRONE. Hermes, Paris.
• OUSTALOUP, A. (1995) La derivation non entiere. Hermes, Paris.
• PODLUBNY, I. (1999) Fractional Differential Equations. Academic Press, San Diego.
• PODLUBNY, I. (2002) Geometric and physical interpretation of fractional integration and fractional differentation. Fract. Calc. Appl. Anal. 5 (4), 367-386.
• PODLUBNY, I., DORCAK, L. and KOSTIAL, I. (1999) On fractional derivatives, fractional order systems and PIλDμ-controllers. Proc. 36th IEEE Conf. Decision and Control, San Diego, CA, 4985-4990.
• SIEROCIUK, D. (2007) Estimation and control of discrete-time fractional systems described by state equations. PhD thesis, Warsaw University of Technology, Warsaw (in Polish).
• SIEROCIUK, D. and DZIELIŃSKI, D. (2006) Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation. Int. J. Appl. Math. Comp. Sci, 16 (1), 129-140.
• VINAGRE, B.M., MONJE, C.A. and CALDERON, A.J. (2002) Fractional order systems and fractional order control actions. Lecture 3 IEEE CDC’02 TW#2: Fractional Calculus Applications in Automatic Control and Robotics.