Old and new perspectives on the positive-real-lemma in systems and controltheory

This essay is based on an invited plenary lecture presented at the 1998 GAM M conference in Bremen, Germany. This was a survey of the historical develo pment of the positive-real lemma, a key result in central theory: from its beginnings in 1962 up to June 1998. Particular emphasis was placed on Me ph ysical motivation and the importance of this lemma to applications in contr ol theory. The inclusion of recent extensions to infinite-dimensional syste ms represents the author's own research interests.