Positive Real Systems

Abstract

The notion of Positive Real system may be seen as a generalization of the positive definiteness of a matrix to the case of a dynamical system with inputs and outputs. When the input-output relation (or mapping, or operator) is a constant matrix, testing its positive definiteness can be done by simply calculating the eigenvalues and checking that they are positive. When the input-output operator is more complex, testing positive realness becomes much more involved. This is the object of this chapter which is mainly devoted to positive real linear time-invariant systems. They are known as PR transfer functions.