Abstract
In this paper the concept of passivity is generalized from the view-point of the rate of energy dissipation, introducing a supply rate with an index γ. A stabilizability result for dissipative systems with the supply rate is obtained. Next, a design method of γ-passive systems is discussed by using a bilinear transformation of nonlinear systems, called Cayley-transform. Finally, in the case of linear systems, it is shown that the index γ can be used as a measure of phase of transfer functions. A shaping method of the phase curve of closed loop transfer functions is also proposed. A generalization of so-called passivity theorem is obtained, which is shown to be effective, by using an example, for analysis of robust stability of feedback systems.
