IEEE Transactions on Automatic Control, Vol.49, No.10, 1875-1877, 2004
Spectral conditions for positive realness of single-input-single-output systems
In this note, we derive necessary and sufficient conditions for a single-input-single-output system to be (strictly) positive real. These conditions take the form of a spectral condition on a matrix product constructed from the state space representation of the linear time-invariant system { A, b, c, d }. Numerical examples are given to illustrate the usefulness of our conditions.
Keywords:Kalman-Yacubovic-Popov;positive real transfer functions;quadratic Lypunov functions;strictly positive real transfer functions