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A comparison of small gain versus Lyapunov type robust stability bounds
Author(s) -
Chen Jie,
Ren Zhang
Publication year - 2001
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/rnc.666
Subject(s) - lyapunov function , singular value , control theory (sociology) , stability (learning theory) , mathematics , state space , lyapunov equation , lyapunov stability , robust control , frequency domain , invariant (physics) , domain (mathematical analysis) , matrix (chemical analysis) , lti system theory , lyapunov exponent , linear system , computer science , nonlinear system , control (management) , mathematical analysis , physics , statistics , chaotic , eigenvalues and eigenvectors , materials science , composite material , quantum mechanics , artificial intelligence , machine learning , mathematical physics
We address stability issues pertaining to perturbed linear time‐invariant systems described by state space models. We show that for a class of highly structured uncertainties in the system matrix, a robust stability bound given by the complex structured singular value is less conservative than that obtained via Lyapunov approach. This result thus provides a counterpart to an earlier one pertaining to unstructured uncertainties, and serves to extend and support the statement that frequency domain small gain conditions may often be less conservative than those time domain criteria obtained using Lyapunov approach. Copyright © 2001 John Wiley & Sons, Ltd.