Positive electrical circuits and their reachability

Open access

Positive electrical circuits and their reachability

Conditions for the positivity of linear electrical circuits composed of resistances, coils, capacitors and voltage (current) sources are established. It is shown that: 1) the electrical circuit composed of resistors, coils and voltage source is positive for any 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.

Antsaklis P. J., Michel A. N., Linear systems. Birkhauser, Boston (2006).

Farina L., Rinaldi S., Positive linear systems; theory and applications. J. Wiley, New York (2000).

Kaczorek T., Decomposition of the pair (A, B) and (A, C) of the positive discrete-time linear systems. Archives of Control Sciences 20(3): 253-273 (2010).

Kaczorek T., Linear control systems. Vol. 1, J. Wiley, New York (1993).

Kaczorek T., Positive 1D and 2D systems. Springer Verlag, London (2001).

Kaczorek T., Reachability and controllability to zero tests for standard and positive fractional discrete-time systems. Journal Européen des Systèmes Automatisés, JESA 42(6-8): 770-781 (2008).

Kailath T., Linear systems. Prentice-Hall, Englewood Cliffs, New York (1980).

Kalman R. E., Mathematical descriptions of linear systems, SIAM J. Control 1: 152-192 (1963).

Kalman R. E., On the General Theory of Control Systems. Proc. of the First Intern. Congress on Automatic Control, Butterworth, London, pp. 481-493 (1960).

Rosenbrock H. H., State-Space and Multivariable Theory. J. Wiley, New York (1970).

Wolovich W. A., Linear Multivariable Systems. Springer-Verlag, New York (1974).

Archives of Electrical Engineering

The Journal of Polish Academy of Sciences

Journal Information

CiteScore 2016: 0.71

SCImago Journal Rank (SJR) 2016: 0.238
Source Normalized Impact per Paper (SNIP) 2016: 0.535


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 137 136 6
PDF Downloads 87 86 4