Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle and Popov theorems and their application to robust stability

Author

Haddad, Wassim M. ; Bernstein, Dennis S.

Author_Institution

Florida Inst. of Technol., Melbourne, FL, USA

fYear

1991

fDate

11-13 Dec 1991

Firstpage

2618

Abstract

Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed

Keywords

Lyapunov methods; stability criteria; transfer functions; Popov theorems; asymptotic stability; circle criterion; feedback interconnections; positive real transfer functions; positive real uncertainty; positively theorem; quadratic Lyapunov functions; robust stability; sector-bounded uncertainty; small gain theorem; strictly proper bounded real transfer functions; time-varying bounded real uncertainty; time-varying memoryless nonlinearity; Asymptotic stability; Electrostatic precipitators; Feedback; Linearity; Lyapunov method; Negative feedback; Robust stability; Stability analysis; Sufficient conditions; Transfer functions; Uncertainty;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1991., Proceedings of the 30th IEEE Conference on

Conference_Location

Brighton

Print_ISBN

0-7803-0450-0

Type

conf

DOI

10.1109/CDC.1991.261825

Filename

261825