LMIs in Control/Matrix and LMI Properties and Tools/Passivity and Positive Realness
This section deals with passivity of a system.
Given a state-space representation of a linear system
are the state, output and input vectors respectively.
are system matrices.
The linear system with the same number of input and output variables is called passive if
hold for any arbitrary , arbitrary input , and the corresponding solution of the system with . In addition, the transfer function matrix
of system is called is positive real if it is square and satisfies
Let the linear system be controllable. Then, the system is passive if an only if there exists such that
This implementation requires Yalmip and Mosek.
Thus, it is seen that passivity and positive-realness describe the same property of a linear system, one gives the time-domain feature and the other provides frequency-domain feature of this property.
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
- LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & Francis Group, 2013