Title :
Spectral conditions for positive realness of single-input-single-output systems
Author :
Shorten, Robert ; King, Christopher
Author_Institution :
Hamilton Inst., Maynooth, Ireland
Abstract :
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 :
Lyapunov methods; linear systems; state-space methods; transfer functions; linear time-invariant systems; positive real transfer functions; quadratic Lyapunov functions; single-input single output systems; spectral conditions; state space representation; Adaptive control; Automatic control; Circuits; Electrical fault detection; Fault diagnosis; Linear matrix inequalities; Robust control; Signal processing; Testing; Transfer functions; Kalman–Yacubovic–Popov; positive real transfer functions; quadratic Lypunov functions; strictly positive real transfer functions;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2004.835593
