Preprint 27-2009

Lyapunov balancing for passivity-preserving model reduction of RC circuits

Author(s) : Timo Reis , Tatjana Stykel

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 27-2009

MSC 2000

93B11 System structure simplification

34A09 Implicit equations, differential-algebraic equations

Abstract :
We apply Lyapunov-based balanced truncation model reduction method to differential-algebraic equations arising in modeling of RC circuits. This method is based on diagonalizing the solution of one projected Lyapunov equation. It is shown that this method preserves passivity and delivers an error bound. By making use of the special structure of circuit equations, we can reduce the numerical effort for balanced truncation drastically.

Keywords : balanced truncation, electrical circuits, Lyapunov equations, model reduction, passivity, positive real, projectors, reciprocity, symmetric systems, differential-algebraic equations