Passivity Margin and Related Bounds for Linear Systems

Author

Psillakis, H.E. ; Alexandridis, A.T.

Author_Institution

Dept. of Electr. & Comput. Eng., Patras Univ.

fYear

2005

fDate

27-29 June 2005

Firstpage

785

Lastpage

790

Abstract

The concept of passivity margin is introduced and analyzed through the Lyapunov equation of the Kalman-Yacubovich-Popov lemma. Furthermore, using an extensive mathematical analysis, bounds for this margin are obtained for both the cases of SISO and MIMO systems. In the first case it is proven that an upper bound of the passivity margin is the minimum of either i) the absolute value of the real part of the maximum stable pole of the system or ii) the difference between the sum of the real parts of all the poles minus the sum of the real parts of all the zeros. In the second case it is proven that bound (ii) is in turn bounded by a logarithmic integral. However, this integral results in an entropy-like expression for SISO systems. Finally, some remarkable comments and an illustrative example are included

Keywords

Lyapunov methods; MIMO systems; entropy; integral equations; linear systems; Lyapunov equation; MIMO systems; SISO systems; entropy-like expression; linear systems; logarithmic integral; passivity margin; related bounds; Helium; Integral equations; Linear systems; MIMO; Mathematical analysis; Poles and zeros; Stability; Transfer functions; Upper bound; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Intelligent Control, 2005. Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation

Conference_Location

Limassol

ISSN

2158-9860

Print_ISBN

0-7803-8936-0

Type

conf

DOI

10.1109/.2005.1467114

Filename

1467114