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. We relate the problem of weighted H∞ control as a special case of this synthesis problem. The synthesis problem and its solution can be systematically understood when one notices that it is similar to finding a non-negative subspace (non-negative with respect to a given constant matrix) within a finite dimensional vector space satisfying certain inclusion and dimension constraints.