An example of a GAS system which can be destabilized by an integrable perturbation

IEEE Transactions on Automatic Control

Volumn 48, Issue 6, 2003, Pages 1046-1049

  Sontag, Eduardo D ^a   Krichman, Mikhail ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Asymptotic stability; Integrable perturbations; Intergral stability

Indexed keywords

CONTROL THEORY; INTEGRAL EQUATIONS; LYAPUNOV METHODS; PERTURBATION TECHNIQUES;

GLOBALLY ASYMPTOTICALLY STABLE (GAS) SYSTEMS;

ASYMPTOTIC STABILITY;

EID: 0037534020     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.812801     Document Type: Article

References (10)

1. D. Angeli, E. D. Sontag, and Y. Wang, "A characterization of integral input to state stability," IEEE Trans. Automat. Contr., vol. 45, pp. 1082-1097, June 2000.
2. _, "Equivalences and semiglobal versions of integral input to state stability," Dyna. Control, vol. 10, pp. 127-149, 2000.
3. M. M. A. El-Sheikh, A. A. Soliman, and M. H. Abd Alla, "On stability of nonlinear systems of ordinary differential equations," Appl. Math. Comput., vol. 113, pp. 175-198, 2000.
4. R. Freeman, "Global internal stabilizability does not imply global external stabilizability for small sensor disturbances," IEEE Trans. Automat. Contr., vol. 40, pp. 2119-2122, Dec. 1995.
5. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities. New York: Academic, 1969, vol. 1.
6. V. Lakshmikantham and X. Liu, "Perturbing families of Liapunov functions and stability in terms of two measures," J. Math. Anal. Appl., vol. 140, pp. 107-114, 1989.
7. L. Praly and M. Arcak, "On certainty-equivalence design of nonlinear observer-based controllers," presented at the 41st IEEE Conf. Decision Control, Las Vegas, NV, Dec. 2002.
8. E. D. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Automat. Contr., vol. 34, pp. 435-443, Apr. 1989.
9. _, "Comments on integral variants of input-to-state stability," Syst. Control Lett., vol. 34, pp. 93-100, 1998.
10. I. Vrkoč, "Integral stability" (in Russian), Czech. Math. J., vol. 9, pp. 71-129, 1958.