Dissipative Systems Synthesis: a Linear Algebraic Approach

In this paper we consider the problem of synthesis of dissipative systems for the case that first and higher order derivatives of the concerned variables also appear in the weighting function. The problem is formulated and solved using the behavioral approach to systems and control. It turns out that this problem can be reformulated analogously as a problem of finding a non-negative subspace (non-negative with respect to a given indefinite constant symmetric matrix) within a finite dimensional vector space satisfying certain inclusion and dimensionality constraints.