American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Coincidence of Lyapunov exponents and central exponents of linear Ito stochastic differential equations with nondegenerate stochastic term
  • PROC Home
  • This Issue
  • Next Article
    Invariant feedback design for control systems with lie symmetries - A kinematic car example
2011, 2011(Special): 322-331. doi: 10.3934/proc.2011.2011.322

A Bohl-Perron type theorem for random dynamical systems

N. D. Cong 1, , T. S. Doan 2, and  S. Siegmund 2,

1. 

Hanoi Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
2. 

Technical University of Dresden, 01069 Dresden, Germany, Germany

Received  July 2010 Revised  March 2011 Published  October 2011

In this paper, a Bohl-Perron type theorem for random dynamical systems is proved which characterizes uniform exponential stability by means of admissibility. As an application, we obtain a lower bound on the stability radius of random dynamical systems based on the norm of the input-output operator.
Keywords: Random dynamical systems, stability radius. The rst author is supported par, Bohl- Perron type theorem, uniform exponential stability.
Mathematics Subject Classification: Primary: 37H05, 37D20; Secondary: 47B80, 39A30.
Citation: N. D. Cong, T. S. Doan, S. Siegmund. A Bohl-Perron type theorem for random dynamical systems. Conference Publications, 2011, 2011 (Special) : 322-331. doi: 10.3934/proc.2011.2011.322
[1]

Weigu Li, Kening Lu. Takens theorem for random dynamical systems. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3191-3207. doi: 10.3934/dcdsb.2016093
[2]

Xiangnan He, Wenlian Lu, Tianping Chen. On transverse stability of random dynamical system. Discrete & Continuous Dynamical Systems, 2013, 33 (2) : 701-721. doi: 10.3934/dcds.2013.33.701
[3]

Weigu Li, Kening Lu. A Siegel theorem for dynamical systems under random perturbations. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 635-642. doi: 10.3934/dcdsb.2008.9.635
[4]

Sigurdur Freyr Hafstein. A constructive converse Lyapunov theorem on exponential stability. Discrete & Continuous Dynamical Systems, 2004, 10 (3) : 657-678. doi: 10.3934/dcds.2004.10.657
[5]

Yongxin Jiang, Can Zhang, Zhaosheng Feng. A Perron-type theorem for nonautonomous differential equations with different growth rates. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 995-1008. doi: 10.3934/dcdss.2017052
[6]

Karl P. Hadeler. Quiescent phases and stability in discrete time dynamical systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 129-152. doi: 10.3934/dcdsb.2015.20.129
[7]

S.Durga Bhavani, K. Viswanath. A general approach to stability and sensitivity in dynamical systems. Discrete & Continuous Dynamical Systems, 1998, 4 (1) : 131-140. doi: 10.3934/dcds.1998.4.131
[8]

Matthew Macauley, Henning S. Mortveit. Update sequence stability in graph dynamical systems. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1533-1541. doi: 10.3934/dcdss.2011.4.1533
[9]

Tomás Caraballo, Stefanie Sonner. Random pullback exponential attractors: General existence results for random dynamical systems in Banach spaces. Discrete & Continuous Dynamical Systems, 2017, 37 (12) : 6383-6403. doi: 10.3934/dcds.2017277
[10]

Gary Froyland, Ognjen Stancevic. Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 457-472. doi: 10.3934/dcdsb.2010.14.457
[11]

Antoine Perasso. Global stability and uniform persistence for an infection load-structured SI model with exponential growth velocity. Communications on Pure & Applied Analysis, 2019, 18 (1) : 15-32. doi: 10.3934/cpaa.2019002
[12]

Gilbert Peralta. Uniform exponential stability of a fluid-plate interaction model due to thermal effects. Evolution Equations & Control Theory, 2020, 9 (1) : 39-60. doi: 10.3934/eect.2020016
[13]

Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete & Continuous Dynamical Systems, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355
[14]

Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete & Continuous Dynamical Systems, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1
[15]

Lei Wang, Zhong-Jie Han, Gen-Qi Xu. Exponential-stability and super-stability of a thermoelastic system of type II with boundary damping. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2733-2750. doi: 10.3934/dcdsb.2015.20.2733
[16]

Pedro Roberto de Lima, Hugo D. Fernández Sare. General condition for exponential stability of thermoelastic Bresse systems with Cattaneo's law. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3575-3596. doi: 10.3934/cpaa.2020156
[17]

Je-Chiang Tsai. Global exponential stability of traveling waves in monotone bistable systems. Discrete & Continuous Dynamical Systems, 2008, 21 (2) : 601-623. doi: 10.3934/dcds.2008.21.601
[18]

Xiang Xie, Honglei Xu, Xinming Cheng, Yilun Yu. Improved results on exponential stability of discrete-time switched delay systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 199-208. doi: 10.3934/dcdsb.2017010
[19]

Daniela Cárcamo-Díaz, Jesús F. Palacián, Claudio Vidal, Patricia Yanguas. Nonlinear stability of elliptic equilibria in hamiltonian systems with exponential time estimates. Discrete & Continuous Dynamical Systems, 2021, 41 (11) : 5183-5208. doi: 10.3934/dcds.2021073
[20]

Henri Schurz. Moment attractivity, stability and contractivity exponents of stochastic dynamical systems. Discrete & Continuous Dynamical Systems, 2001, 7 (3) : 487-515. doi: 10.3934/dcds.2001.7.487

 Impact Factor: 

Tools

Metrics

  • PDF downloads (77)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy