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Improved condition for stabilization of controlled inverted pendulum under stochastic perturbations
| 1. | Department of Higher Mathematics, Donetsk State University of Management, Chelyuskintsev str., 163-a, Donetsk, 83015 |
| [1] |
Mari Paz Calvo, Jesus M. Sanz-Serna. Carrying an inverted pendulum on a bumpy road. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 429-438. doi: 10.3934/dcdsb.2010.14.429 |
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Roman Srzednicki. On periodic solutions in the Whitney's inverted pendulum problem. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2127-2141. doi: 10.3934/dcdss.2019137 |
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Ivan Polekhin. On motions without falling of an inverted pendulum with dry friction. Journal of Geometric Mechanics, 2018, 10 (4) : 411-417. doi: 10.3934/jgm.2018015 |
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Hjörtur Björnsson, Sigurdur Hafstein, Peter Giesl, Enrico Scalas, Skuli Gudmundsson. Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4247-4269. doi: 10.3934/dcdsb.2019080 |
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Tomás Caraballo, Leonid Shaikhet. Stability of delay evolution equations with stochastic perturbations. Communications on Pure and Applied Analysis, 2014, 13 (5) : 2095-2113. doi: 10.3934/cpaa.2014.13.2095 |
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Yubai Liu, Xueshan Gao, Fuquan Dai. Implementation of Mamdami fuzzy control on a multi-DOF two-wheel inverted pendulum robot. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1251-1266. doi: 10.3934/dcdss.2015.8.1251 |
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Paweł Góra, Abraham Boyarsky. Stochastic perturbations and Ulam's method for W-shaped maps. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1937-1944. doi: 10.3934/dcds.2013.33.1937 |
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Guillaume Bal, Olivier Pinaud, Lenya Ryzhik. On the stability of some imaging functionals. Inverse Problems and Imaging, 2016, 10 (3) : 585-616. doi: 10.3934/ipi.2016013 |
| [9] |
Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki. Lyapunov functionals for multistrain models with infinite delay. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 507-536. doi: 10.3934/dcdsb.2017025 |
| [10] |
Chao Liang, Wenxiang Sun, Jiagang Yang. Some results on perturbations of Lyapunov exponents. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4287-4305. doi: 10.3934/dcds.2012.32.4287 |
| [11] |
Victor Berdichevsky. Distribution of minimum values of stochastic functionals. Networks and Heterogeneous Media, 2008, 3 (3) : 437-460. doi: 10.3934/nhm.2008.3.437 |
| [12] |
Sergio Grillo, Jerrold E. Marsden, Sujit Nair. Lyapunov constraints and global asymptotic stabilization. Journal of Geometric Mechanics, 2011, 3 (2) : 145-196. doi: 10.3934/jgm.2011.3.145 |
| [13] |
Jihoon Lee, Nguyen Thanh Nguyen. Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1263-1296. doi: 10.3934/cpaa.2021020 |
| [14] |
Tomoharu Suda. Construction of Lyapunov functions using Helmholtz–Hodge decomposition. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2437-2454. doi: 10.3934/dcds.2019103 |
| [15] |
Peter Giesl, Sigurdur Hafstein. System specific triangulations for the construction of CPA Lyapunov functions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6027-6046. doi: 10.3934/dcdsb.2020378 |
| [16] |
Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki. Lyapunov functionals for virus-immune models with infinite delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 3093-3114. doi: 10.3934/dcdsb.2015.20.3093 |
| [17] |
Pierre Guiraud, Etienne Tanré. Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 5183-5201. doi: 10.3934/dcdsb.2019056 |
| [18] |
Leonid Shaikhet. Stability of delay differential equations with fading stochastic perturbations of the type of white noise and poisson's jumps. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3651-3657. doi: 10.3934/dcdsb.2020077 |
| [19] |
Guoshan Zhang, Peizhao Yu. Lyapunov method for stability of descriptor second-order and high-order systems. Journal of Industrial and Management Optimization, 2018, 14 (2) : 673-686. doi: 10.3934/jimo.2017068 |
| [20] |
Luigi Ambrosio, Camillo Brena. Stability of a class of action functionals depending on convex functions. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022055 |
2020 Impact Factor: 1.392
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