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A constructive converse Lyapunov theorem on exponential stability
1.  Department of Theoretical Physics, GerhardMercatorUniversity, Duisburg, D47057, Germany 
[1] 
Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of firstorder ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 281298. doi: 10.3934/dcdsb.2014.19.281 
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Michael Schönlein. Asymptotic stability and smooth Lyapunov functions for a class of abstract dynamical systems. Discrete & Continuous Dynamical Systems  A, 2017, 37 (7) : 40534069. doi: 10.3934/dcds.2017172 
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Christopher M. Kellett. Classical converse theorems in Lyapunov's second method. Discrete & Continuous Dynamical Systems  B, 2015, 20 (8) : 23332360. doi: 10.3934/dcdsb.2015.20.2333 
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Luis Barreira, Claudia Valls. Stability of nonautonomous equations and Lyapunov functions. Discrete & Continuous Dynamical Systems  A, 2013, 33 (7) : 26312650. doi: 10.3934/dcds.2013.33.2631 
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Volodymyr Pichkur. On practical stability of differential inclusions using Lyapunov functions. Discrete & Continuous Dynamical Systems  B, 2017, 22 (5) : 19771986. doi: 10.3934/dcdsb.2017116 
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Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sumofsquares programming. Discrete & Continuous Dynamical Systems  B, 2018, 23 (2) : 939956. doi: 10.3934/dcdsb.2018049 
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Huijuan Li, Robert Baier, Lars Grüne, Sigurdur F. Hafstein, Fabian R. Wirth. Computation of local ISS Lyapunov functions with low gains via linear programming. Discrete & Continuous Dynamical Systems  B, 2015, 20 (8) : 24772495. doi: 10.3934/dcdsb.2015.20.2477 
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Jean Mawhin, James R. Ward Jr. Guidinglike functions for periodic or bounded solutions of ordinary differential equations. Discrete & Continuous Dynamical Systems  A, 2002, 8 (1) : 3954. doi: 10.3934/dcds.2002.8.39 
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Robert Baier, Lars Grüne, Sigurđur Freyr Hafstein. Linear programming based Lyapunov function computation for differential inclusions. Discrete & Continuous Dynamical Systems  B, 2012, 17 (1) : 3356. doi: 10.3934/dcdsb.2012.17.33 
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Tomasz Kapela, Piotr Zgliczyński. A Lohnertype algorithm for control systems and ordinary differential inclusions. Discrete & Continuous Dynamical Systems  B, 2009, 11 (2) : 365385. doi: 10.3934/dcdsb.2009.11.365 
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Fuke Wu, George Yin, Le Yi Wang. Razumikhintype theorems on moment exponential stability of functional differential equations involving twotimescale Markovian switching. Mathematical Control & Related Fields, 2015, 5 (3) : 697719. doi: 10.3934/mcrf.2015.5.697 
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Stefano Maset. Conditioning and relative error propagation in linear autonomous ordinary differential equations. Discrete & Continuous Dynamical Systems  B, 2018, 23 (7) : 28792909. doi: 10.3934/dcdsb.2018165 
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Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control & Related Fields, 2018, 8 (3&4) : 809828. doi: 10.3934/mcrf.2018036 
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Doan Thai Son. On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31133126. doi: 10.3934/dcdsb.2017166 
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Frédéric Mazenc, Christophe Prieur. Strict Lyapunov functions for semilinear parabolic partial differential equations. Mathematical Control & Related Fields, 2011, 1 (2) : 231250. doi: 10.3934/mcrf.2011.1.231 
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Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discretetime state observations. Discrete & Continuous Dynamical Systems  B, 2017, 22 (1) : 209226. doi: 10.3934/dcdsb.2017011 
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Yuriy Golovaty, Anna MarciniakCzochra, Mariya Ptashnyk. Stability of nonconstant stationary solutions in a reactiondiffusion equation coupled to the system of ordinary differential equations. Communications on Pure & Applied Analysis, 2012, 11 (1) : 229241. doi: 10.3934/cpaa.2012.11.229 
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Leonid Berezansky, Elena Braverman. Stability of linear differential equations with a distributed delay. Communications on Pure & Applied Analysis, 2011, 10 (5) : 13611375. doi: 10.3934/cpaa.2011.10.1361 
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A. Domoshnitsky. About maximum principles for one of the components of solution vector and stability for systems of linear delay differential equations. Conference Publications, 2011, 2011 (Special) : 373380. doi: 10.3934/proc.2011.2011.373 
[20] 
Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic meansquare stability properties for systems of linear stochastic delay differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 15211531. doi: 10.3934/dcdsb.2013.18.1521 
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