Notions of exponential robust stochastic stability, ISS and their Lyapunov characterizations

International Journal of Robust and Nonlinear Control

Volumn 13, Issue 2, 2003, Pages 173-187

  Spiliotis, J ^a   Tsinias, J ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

ISS; Lyapunov functions; Robust stochastic stability

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; THEOREM PROVING;

WIENER PROCESSES;

STOCHASTIC CONTROL SYSTEMS;

EID: 0037317805     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.724     Document Type: Article

References (14)

1. Tsinias J., Spiliotis J. A Converse Lyapunov Theorem for Robust Exponential Stochastic Stability, Lecture Notes in Control and Information Sciences, vol. 246, Workshop of the Nonlinear Control, Ghent. Springer: Berlin, 1999; 355-374.
2. Arnold L. Stochastic Differential Equations, Theory and Applications. Wiley: New York, 1974.
3. Krylov NV. Controlled Diffusion Processes. Springer: Berlin, 1980.
4. Oksendal B. Stochastic Differential Equations. Springer: Berlin, 1985.
5. Lin Y, Sontag ED, Wang Y. A smooth converse Lyapunov theorem for robust stability. SIAM Journal of Control and Optimization 1996; 34:124-160.
6. n. Communications on Pure and Applied Mathematica 1980; XXXIV:121-147.
7. Khalil H. Nonlinear Systems. Prentice-Hall: 1996.
8. Kushner J. Stochastic Stability and Control. Academic Press: New York, 1967.
9. Khasminskii RZ. Stochastic Stability of Differential Equations. Sijithoff & Noordhaff, Alphen a/d Rijn, 1980.
10. Sontag ED, Wang Y. On characterizations of input-to-state stability properties. Systems and Control Letters 1995; 24:226-231.
11. Tsinias J. Input-to-state stability properties of nonlinear systems and applications to bounded feedback stabilization using saturation. COCV-ESAIM, 2, 7, 1997.
12. Krstic M, Deng H. Stabilization of Nonlinear Uncertain Systems. Springer: Berlin, 1998.
13. Tsinias J. Stochastic input-to-state stability and applications to global feedback stabilization. International Journal of Control [special issue 'Recent advances in the control of nonlinear systems, F. Lamnabhi-Lagarrigue (ed.)] 1998; 71(5):907-931.
14. Tsinias J. The concept of 'exponential ISS' for stochastic systems and applications to feedback stabilization. Systems and Control Letters 1999; 36:221-229.