Multidimensional causality and passivity of linear and nonlinear systems arising from physics

Authors:	Alfred Fettweis	Lehrstuhl fuer Nachrichetntechnik, Ruhr Universitaet, Bochum, Germany 44780
	Sankar Basu	National Science Foundation, Arlington, USA 22101

Published in:

· Journal

Multidimensional Systems and Signal Processing archive

Volume 22 Issue 1-3, March 2011
Kluwer Academic Publishers Hingham, MA, USA
table of contents doi>10.1007/s11045-010-0135-y

We start with the general notions of causality, passivity, losslessness and related concepts for a class of multidimensional systems, in particular with multidimensional causality and passivity, arising from physical considerations. While such definitions are nowhere restricted to linear systems we show that when applied to linear systems with constant parameters (coefficients) they boil down to standard notions of passivity described by positive real functions and matrices, or equivalently, by bounded real functions and matrices in several complex variables.