External and internal stabilization under the presence of stochastic disturbances

  • Ali Saberi
  • Anton A. Stoorvogel
  • Peddapullaiah Sannuti
Part of the Systems & Control: Foundations & Applications book series (SCFA)


So far, all the results discussed in this book are in deterministic setting. A new frontier for the next phase of research is in stochastic setting. That is, to consider disturbances which are modeled as colored noise which in turn can be modeled as white noise followed by a linear system. Then, the goal is to investigate simultaneous external and internal stabilization of linear systems subject to constraints when the disturbances are modeled stochastically.


Wiener Process Colored Noise Internal Stabilization Null Controllable Gaussian Random Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 109.
    B. Øksendal, Stochastic differential equations: an introduction with applications, Universitext, Springer-Verlag, Berlin, Sixth Ed., 2003.Google Scholar
  2. 113.
    R. Pemantle and J.S. Rosenthal, “Moment conditions for a sequence with negative drift to be uniformly bounded in L r”, Stochastic Processes and their Applications, 82(1), 1999, pp. 143–155.Google Scholar
  3. 116.
    F. Ramponi, D. Chatterjee, A. Milias-Argeitis, P. Hokayem, and J. Lygeros, “Attaining mean square boundedness of a neutrally stable noisy linear system with a bounded control input”, IEEE Trans. Aut. Contr., 55(10), 2010, pp. 2414–2418.MathSciNetCrossRefGoogle Scholar
  4. 165.
    A. Stoorvogel and A. Saberi, “On external semi-global stochastic stabilization of a double integrator with input saturation”, in Proc. 47th CDC, Cancun, Mexico, 2008, pp. 3493–3497.Google Scholar
  5. 168.
    A.A. Stoorvogel, A. Saberi, and S. Weiland, “On external semi-global stochastic stabilization of linear systems with input saturation”, in American Control Conference, New York, 2007, pp. 5845–5850.Google Scholar
  6. 171.
    A.A. Stoorvogel, S. Weiland, and A. Saberi, “On stabilization of linear systems with stochastic disturbances and input saturation”, in Proc. 43rd CDC, The Bahamas, 2004, pp. 3007–3012.Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Ali Saberi
    • 1
  • Anton A. Stoorvogel
    • 2
  • Peddapullaiah Sannuti
    • 3
  1. 1.School of Electrical Engineering and Computer ScienceWashington State UniversityPullmanUSA
  2. 2.Department of Electrical Engineering, Mathematics, and Computer ScienceUniversity of TwenteEnschedeThe Netherlands
  3. 3.Department of Electrical and Computer EngineeringRutgers UniversityPiscatawayUSA

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