Selected classes of positive electrical circuits and their reachability

• Autorzy: Kaczorek T.
• Konferencja: Computer Applications in Electrical Engineering 2012 (23-24.04.2012; Poznań, Polska)
• Języki publikacji: EN

Abstrakty

EN

Conditions for the positivity of linear electrical circuits composed of resistors, coils, condensators and voltage (current) sources are established. It is shown that: 1) the electrical circuit composed of resistors, coils and voltage source is positive for almost all values of their resistances, inductances and source voltages if and only if the number of coils is less or equal to the number of its linearly independent meshes, 2) the electrical circuit is not positive for any values of its resistances, capacitances and source voltages if each its branch contains resistor, capacitor and voltage source, 3) the positive n-meshes electrical circuit with only one inductance in each linearly independent mesh is reachable if all resistances of branches belonging to two linearly independent meshes are zero 4) the electrical circuits of the structure shown on Fig.5.2 is reachable if and only if the condition (5.11) is satisfied.

Słowa kluczowe

EN

electrical circuits; Metzler matrix; linear system

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Computer Applications in Electrical Engineering
• Rocznik: 2012
• Tom: Vol. 10
• Strony: 1--28
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Kaczorek T.

• Bialystok University of Technology 15-351 Bialystok, Wiejska 45D

Bibliografia

• [1] P.J. Antsaklis, A.N. Michel, Linear Systems, Birkhauser, Boston 2006.
• [2] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [3] T. Kaczorek, Decomposition of the pair (A,5) and (A,C) of the positive discrete-time linear systems, Archives of Control Sciences, Vol. 20, No. 3, 2010, 253-273.
• [4] T. Kaczorek, Linear Control Systems, Vol. 1, J. Wiley, New York 1993.
• [5] T. Kaczorek, Positive 1D and 2D systems, Springer Verlag, London 2001.
• [6] T. Kaczorek, Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, Journal Europeen des Systemes Automatises, JESA, Vol. 42, No. 6-8, 2008, 770-781.
• [7] T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, New York 1980.
• [8] R.E. Kalman, Mathematical Descriptions of Linear Systems, SIAM J. Control, Vol. 1, 1963, 152-192.
• [9] R.E. Kalman, On the General Theory of Control Systems, Proc. Of the First Intern. Congress on Automatic Control, Butterworth, London, 1960, 481-493.
• [10] H.H. Rosenbrock, State-Space andMultivariable Theory, J. Wiley, New York 1970.
• [11] W.A. Wolovich, Linear Multivariable Systems, Springer-Verlag New York 1974.