STRICTLY POSITIVE REAL ADMITTANCES FOR COUPLED STABILITY

This paper builds upon recent work that has addressed the stability of a feedback-controlled robot coupled to a passive, dynamic environment. A new definition of a "strictly positive real" function is presented, and is used to provide necessary and sufficient conditions for the exponential stability of a coupled system comprising a 1-port robot with a strictly positive real admittance, and a 1-port environment with a positive real (but otherwise arbitrary) impedance. The distinction between the new definition and conventional definitions of a strictly positive real function is founded in physical systems theory: the new definition relies upon distinct roles for efforts and flows, and upon the concept of an excess state. This definition will provide a useful design constraint for the development of robust robot controllers.