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Guaranteed domains of attraction for multivariable Luré systems via open Lyapunov surfaces
Author(s) -
Haddad Wassim M.,
Kapila Vikram,
Chellaboina VijayaSekhar
Publication year - 1997
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199710)7:10<935::aid-rnc255>3.0.co;2-b
Subject(s) - lyapunov function , multivariable calculus , control theory (sociology) , mathematics , lyapunov redesign , nonlinear system , computation , invariant (physics) , bounded function , control lyapunov function , domain (mathematical analysis) , computer science , mathematical analysis , control (management) , control engineering , engineering , algorithm , physics , quantum mechanics , artificial intelligence , mathematical physics
In this paper we provide guaranteed stability regions for multivariable Luré‐type systems. Specifically, using the Luré–Postnikov Lyapunov function a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time‐invariant system and whose feedback path contains multiple sector‐bounded time‐invariant memoryless nonlinearities is constructed via open Lyapunov surfaces. It is shown that the use of open Lyapunov surfaces yields a considerable improvement over closed Lyapunov surfaces in estimating the domain of attraction of the zero solution of the nonlinear system. An immediate application of this result is the computation of transient stability regions for multimachine power systems and computation of stability regions of anti‐windup controllers for systems subject to input saturation. © 1997 by John Wiley & Sons, Ltd.