Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stabilityLyapunov 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: (1) a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and (2) 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.
Document ID
19930029194
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Haddad, Wassim M. (Florida Inst. of Technology Melbourne, United States)
Bernstein, Dennis S. (Michigan Univ. Ann Arbor, United States)
Date Acquired
August 15, 2013
Publication Date
January 1, 1991
Publication Information
Publication: In: IEEE Conference on Decision and Control, 30th, Brighton, United Kingdom, Dec. 11-13, 1991, Proceedings. Vol. 3 (A93-13001 02-63)
Publisher: Institute of Electrical and Electronics Engineers, Inc.