System characterization of positive real conditions

Abstract

Necessary and sufficient conditions for positive realness in terms of state-space matrices are presented under the assumption of complete controllability and complete observability of square systems with independent inputs. By a particular transform of these conditions, a direct algorithm for testing positive realness is determined that requires only checking a set of simple algebraic conditions. This provides an alternative procedure to the positive real lemma and to the s-domain inequalities. Based on this algorithm, a synthesis of a positive real system via output feedback is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>