Positive discrete-time linear Lyapunov systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

The notion of positive discrete-time Lyapunov system is introduced. Solution of the Lyapunov state equation is derived and necessary and sufficient conditions for the positivity of Lyapunov system are established. Different necessary and sufficient conditions for the asymptotic stability of the positive Lyapunov systems are given. Using the Kronecker product of matrices necessary and sufficient conditions for reachability and controllability of the positive Lyapunov systems are established. The considerations are illustrated by numerical example.

Słowa kluczowe

EN

Lyapunov; positive; realization

• Wydawca: Łukasiewicz Industrial Research Institute for Automation and Measurements PIAP
• Czasopismo: Journal of Automation Mobile Robotics and Intelligent Systems
• Rocznik: 2008
• Tom: Vol. 2, No. 3
• Strony: 13--19
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] L Berwenuti and L. Farina, "A tutorial on the positive realization problem", IEEE Trans. Autom. Control, vol. 49, no. 5, 2004, pp. 651-664.
• [2] M. Busłowicz and T. Kaczorek, "Reachability and mini­mum energy control of positive linear discrete-time sys­tems with one delay", 12th Mediterranean Conference on Control and Automation, 6th-9th June 2004, Kusadasi, Izmir, Turkey.
• [3] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley: New York, 2000.
• [4] T. Kaczorek, Positive ID and 20 systems, Springer Verlag: London 2001.
• [5] T. Kaczorek, Vectors and Matrices in Automation and Electrotechnics, Publ.: Wydawnictwo Naukowo-Technicznef Warszawa 1998 (in Polish).
• [6] T. Kaczorek, "New reachability and observability tests for positive linear discrete-time systems", Bull. Poll. Acad. Sci. Techn., vol. 55, no. 1, 2007.
• [7] T. Kaczorek, "Realization problem for positive discrete-time systems with delay", System Sciencef vol. 30, no. 4, 2004,pp.117-130.
• [8] T. Kaczorek, „Realization problem for positive multivariable discret-time linear systems with delays in the state vector and inputs", Int. J. Appl. Math. Comp. Sd., vol. 16, no. 2, 2006, pp. 101-106.
• [9] T. Kaczorek, "A realization problem for positive conti-nuous-time systems with reduced numbers of delays", Int. J. Appl. Math. Comp. Sci., vol 16, no. 3, 2006, pp. 101-117.
• [10] T. Kaczorek and M. Bustowicz, "Minimal realization problem for positive multivariable linear systems with delay", Int. J. Appl. Math. Comput. Sci., vol. 14, no. 2, 2004, pp.181-187.
• [11] M.S.N. Murty and B.V. Apparao, "Controllability and observability of Lyapunov systems", Ranchi University Mathematical Journal, vol.32,2005, pp. 55-65.