Characterization and partial synthesis of the behavior of resistive circuits at their terminals

Abstract The external behavior of linear resistive circuits with terminals is characterized as a linear input–output map given by a weighted Laplacian matrix. Conditions are derived for shaping the external behavior of the circuit by interconnection with an additional resistive circuit.

[1]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[2]  J. Willems,et al.  Synthesis of dissipative systems using quadratic differential forms: part II , 2002, IEEE Trans. Autom. Control..

[3]  P. Bamberg,et al.  A course in mathematics for students of physics , 1990 .

[4]  Jan C. Willems,et al.  The behavior of resistive circuits , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[5]  J. Willems.  The Behavioral Approach to Open and Interconnected Systems , 2007, IEEE Control Systems.

[6]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[7]  G. Kirchhoff.  Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird , 1847 .

[8]  J. Willems.  On interconnections, control, and feedback , 1997, IEEE Trans. Autom. Control..

[9]  Arjan van der Schaft,et al.  Achievable behavior of general systems , 2003, Syst. Control. Lett..

[10]  Arjan van der Schaft,et al.  Conservation Laws and Lumped System Dynamics , 2009 .

[11]  Arjan van der Schaft,et al.  Interconnection of port-Hamiltonian systems and composition of Dirac structures , 2007, Autom..

[12]  H. Narayanan.  Some applications of an Implicit Duality Theorem to connections of structures of special types including Dirac and reciprocal structures , 2002, Syst. Control. Lett..

[13]  Joost Rommes,et al.  Efficient Methods for Large Resistor Networks , 2010, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[14]  William L. Burke,et al.  A Course in Mathematics for Students of Physics: Volume 1 , 1988 .