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A constructive converse Lyapunov theorem on exponential stability
1.  Department of Theoretical Physics, GerhardMercatorUniversity, Duisburg, D47057, Germany 
[1] 
Michael Schönlein. Asymptotic stability and smooth Lyapunov functions for a class of abstract dynamical systems. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 40534069. doi: 10.3934/dcds.2017172 
[2] 
Bin Wang, Arieh Iserles. Dirichlet series for dynamical systems of firstorder ordinary differential equations. Discrete and Continuous Dynamical Systems  B, 2014, 19 (1) : 281298. doi: 10.3934/dcdsb.2014.19.281 
[3] 
Christopher M. Kellett. Classical converse theorems in Lyapunov's second method. Discrete and Continuous Dynamical Systems  B, 2015, 20 (8) : 23332360. doi: 10.3934/dcdsb.2015.20.2333 
[4] 
Luis Barreira, Claudia Valls. Stability of nonautonomous equations and Lyapunov functions. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 26312650. doi: 10.3934/dcds.2013.33.2631 
[5] 
Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sumofsquares programming. Discrete and Continuous Dynamical Systems  B, 2018, 23 (2) : 939956. doi: 10.3934/dcdsb.2018049 
[6] 
Volodymyr Pichkur. On practical stability of differential inclusions using Lyapunov functions. Discrete and Continuous Dynamical Systems  B, 2017, 22 (5) : 19771986. doi: 10.3934/dcdsb.2017116 
[7] 
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 and Continuous Dynamical Systems  B, 2015, 20 (8) : 24772495. doi: 10.3934/dcdsb.2015.20.2477 
[8] 
Robert Baier, Lars Grüne, Sigurđur Freyr Hafstein. Linear programming based Lyapunov function computation for differential inclusions. Discrete and Continuous Dynamical Systems  B, 2012, 17 (1) : 3356. doi: 10.3934/dcdsb.2012.17.33 
[9] 
Janusz Mierczyński, Sylvia Novo, Rafael Obaya. Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 22352255. doi: 10.3934/cpaa.2020098 
[10] 
Jean Mawhin, James R. Ward Jr. Guidinglike functions for periodic or bounded solutions of ordinary differential equations. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 3954. doi: 10.3934/dcds.2002.8.39 
[11] 
Serge Nicaise. Stability and asymptotic properties of dissipative evolution equations coupled with ordinary differential equations. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021057 
[12] 
Tomasz Kapela, Piotr Zgliczyński. A Lohnertype algorithm for control systems and ordinary differential inclusions. Discrete and Continuous Dynamical Systems  B, 2009, 11 (2) : 365385. doi: 10.3934/dcdsb.2009.11.365 
[13] 
Fuke Wu, George Yin, Le Yi Wang. Razumikhintype theorems on moment exponential stability of functional differential equations involving twotimescale Markovian switching. Mathematical Control and Related Fields, 2015, 5 (3) : 697719. doi: 10.3934/mcrf.2015.5.697 
[14] 
Peter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur Hafstein. Computing complete Lyapunov functions for discretetime dynamical systems. Discrete and Continuous Dynamical Systems  B, 2021, 26 (1) : 299336. doi: 10.3934/dcdsb.2020331 
[15] 
Stefano Maset. Conditioning and relative error propagation in linear autonomous ordinary differential equations. Discrete and Continuous Dynamical Systems  B, 2018, 23 (7) : 28792909. doi: 10.3934/dcdsb.2018165 
[16] 
William Guo. The Laplace transform as an alternative general method for solving linear ordinary differential equations. STEM Education, 2021, 1 (4) : 309329. doi: 10.3934/steme.2021020 
[17] 
Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control and Related Fields, 2018, 8 (3&4) : 809828. doi: 10.3934/mcrf.2018036 
[18] 
Doan Thai Son. On analyticity for Lyapunov exponents of generic bounded linear random dynamical systems. Discrete and Continuous Dynamical Systems  B, 2017, 22 (8) : 31133126. doi: 10.3934/dcdsb.2017166 
[19] 
Frédéric Mazenc, Christophe Prieur. Strict Lyapunov functions for semilinear parabolic partial differential equations. Mathematical Control and Related Fields, 2011, 1 (2) : 231250. doi: 10.3934/mcrf.2011.1.231 
[20] 
Zhiling Guo, Shugen Chai. Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022001 
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