Positive continuous-time linear time-varying Lyapunov systems

• Autorzy: Kaczorek T. , Przyborowski P.
• Języki publikacji: EN

Abstrakty

EN

The notion of positive continuous-time time-varying Lyapunov system is introduced. Necessary and sufficient conditions for the positivity and the asymptotic stability of the systems are established. Sufficient conditions for reachability are given and the Cayley-Hamilton theorem is extended for time-varying Lyapunov systems. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

positivity; Lyapunov systems; time-varying systems; Cayley-Hamilton theorem

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2007
• Tom: Vol. 33, no 4
• Strony: 5--12
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Kaczorek T.

autor

Przyborowski P.

• Institute of Control and Industrial Electronics, Warsaw Technical University, Koszykowa 75, 00-662 Warsaw, Poland,

Bibliografia

• [1] Benvenuti L., Farina L., A tutorial on positive realization problem, IEEE Trans. Autom. Control, Vol. 49, No. 5, 2004, pp. 651-664.
• [2] Busłowicz M., Kaczorek T., Reachability and minimum energy control of positive linear discrete-lime systems with one delay, 12th Mediterranean Conf. Control and Automation, June 6-9, 2004, Kusadasi, Izmir, Turkey.
• [3] Farina L., Rinaldi S., Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [4] Kaczorek T., Positive ID and 2D systems. Springer Verlag, London, 2001.
• [5] Kaczorek T., Vectors and Matrices in Automation and Electrotechnics, Wydawnictwo Naukowo-Techniczne, Warszawa, 1998, (in Polish).
• [6] Kaczorek T., New reachability and observability tests for positive linear discrete-time systems, Bull. Pol. Acad. Sci. Techn., Vol. 55, No. 1, 2007.
• [7] Kaczorek T., Realization problem for positive discrete-time systems with delay. System Science, Vol. 30. No. 4, 2004, pp. 117-130.
• [8] Kaczorek T., Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs, Int. J. Appl. Math. Comp. Sci., Vol. 16, No. 2, 2006, pp. 101-106.
• [9] Kaczorek T., A realization problem for positive continuous-time systems with reduced number of delays. Int. J. Appl. Math. Comp. Sci., Vol. 16, No. 3, 2006, pp. 101-117.
• [10] Kaczorek T., Externally and internally positive time-varying linear systems, Int. J. Appl. Math. Comput. Sci., Vol. 11, No. 4, 2001, pp. 957-964.
• [11] Kaczorek T., Positive discrete-time linear Lyapunov systems, submitted to The 15th Mediterranean Conf. Control and Automation - MED 2007. 27-29 June, Athens.
• [12] Kaczorek T., Busłowicz M., Minimal realization problem for positive multivariable linear systems with delay. Int. J. Appl. Math. Comp. Sci., Vol. 14. No. 2, 2004, pp. 181-187.
• [13] Kaczorek T., Przyborowski P., Positive continuous-time linear Lyapunov systems, submitted to The International Conference on Computer as a Tool EUROCON 2007, 9-12 September, Warsaw.
• [14] Murty M.S.N., Apparao B.V., Controllability and observability of Lyapunov systems, Ranchi University Mathematical Journal, Vol. 32, 2005. pp. 55-65.
• [15] Wu Min-Yen, On stability of linear time-varying systems. Int. J. Systems Science. Vol. 15. No. 2. 1984, pp. 137-150.