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We propose a novel operator-theoretic framework to study global stability of nonlinear systems.
Application de la théorie des équations integrales lineaires aux systèmes d’équations différentielles nonlinéaires
T. Carleman · 1932
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Chaos, Fractals, and Noise: stochastic aspects of dynamics
A. Lasota and M. C. Mackey · 1994
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Spectral signature of the pitchfork bifurcation: Liouville equation approach
P. Gaspard, G. Nicolis, A. Provata, and S. Tasaki · 1995
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Nonlinear systems
H. K. Khalil and J. W. Grizzle · 1996
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Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
P. A. Parrilo · 2000
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Liouvillian dynamics of the Hopf bifurcation
P. Gaspard and S. Tasaki · 2001
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A dual to Lyapunov’s stability theorem
A. Rantzer · 2001
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Spectral properties of dynamical systems, model reduction and decompositions
I. Mezić · 2005
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Lyapunov measure for almost everywhere stability
U. Vaidya and P. G. Mehta · 2008
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Moments, positive polynomials and their applications
J.-B. Lasserre · 2009
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Spectral analysis of nonlinear flows
C. W. Rowley, I. Mezic, S. Bagheri, P. Schlatter, and D. S. Henningson · 2009
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Stability in the almost everywhere sense: A linear transfer operator approach
R. Rajaram, U. Vaidya, M. Fardad, and B. Ganapathysubramanian · 2010
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Applied Koopmanism
M. Budišić, R. Mohr, and I. Mezić · 2012
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The Bernstein polynomial basis: A centennial retrospective
R. T. Farouki · 2012
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Linearization in the large of nonlinear systems and Koopman operator spectrum
Y. Lan and I. Mezić · 2013
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A spectral operator-theoretic framework for global stability
A. Mauroy and I. Mezić · 2013
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Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics
A. Mauroy, I. Mezić, and J. Moehlis · 2013
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Analysis of fluid flows via spectral properties of Koopman operator
I. Mezić · 2013
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A differential Lyapunov framework for contraction analysis
F. Forni and R. Sepulchre · 2014
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Nonlinear Koopman modes and power system stability assessment without models
Y. Susuki and I. Mezić · 2014
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On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
A. Mauroy and I. Mezić · 2012
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Controller design and region of attraction estimation for nonlinear dynamical systems
M. Korda, D. Henrion, and C. N. Jones · 2013
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R. Mohr and I. Mezić
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A kernel approach to data-driven Koopman spectral analysis
M. O. Williams, C. W. Rowley, and I. G. Kevrekidis · 2014
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A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
M. O. Williams, I. G. Kevrekidis, and C. W. Rowley · 2015
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