Uniform global asymptotic stability of differential inclusions

Journal of Dynamical and Control Systems

Volumn 10, Issue 3, 2004, Pages 391-412

  Angeli, D ^a   Ingalls, B ^b   Sontag, E D ^c   Wang, Y ^d  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF WATERLOO   (Canada)

^c RUTGERS UNIVERSITY   (United States)

^d FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

Control systems; Differential inclusions; Partial detectability; Stability

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; CONFORMAL MAPPING; CONTROL SYSTEM ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ERROR DETECTION; FUNCTIONS; LYAPUNOV METHODS; SET THEORY; STATE SPACE METHODS; THEOREM PROVING;

DIFFERENTIAL INCLUSIONS; GLOBAL ERROR DETECTABILITY; PARTIAL DETECTABILITY; STANDARD RELAXATION THEOREM; UNIFORM GLOBAL ASYMPTOTIC STABILITY;

SYSTEM STABILITY;

EID: 3142680933     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JODS.0000034437.54937.7f     Document Type: Article

References (18)

1. F. Albertini and E. D. Sontag, Continuous control-Lyapunov functions for asymptotically controllable time-varying systems. Int. J. Control 72 (1999), 1630-1641.
2. D. Angeli, B. Ingalls, E. D. Sontag, and Y. Wang, Asymptotic characterizations of IOSS. Proc. IEEE Conf. Decision and Control (2001), 881-886.
3. D. Angeli and E. D. Sontag, Forward completeness, unboundedness observability, and their Lyapunov characterizations. Systems Control Lett. 38 (1999), 209-217.
4. J.-P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag, Berlin (1984).
5. J.-P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhäuser, Boston (1990).
6. F. H. Clarke, Yu Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York (1998).
7. R. M. Colombo, A. Fryszkowski, T. Rzežuchowski, and V. Staicu, Continuous Selections of Solution Sets of Lipschitzian Differential Inclusions. Funkcial. Ekvac. 34 (1991), 321-330.
8. K. Deimling, Multivalued Differential Equations. Walter De Gruyter, Berlin (1992).
9. A. F. Filippov, Differential Equations with Discontinuous Right-hand Sides. Kluwer Academic, Dordrecht (1988).
10. A. Fryszkowski and T. Rzežuchowski, Continuous version of Filippov-Wažewski relaxation theorem. J. Differential Equations 94 (1991), 254-265.
11. B. Ingalls, E. D. Sontag, and Y. Wang, Generalizations of asymptotic gain characterizations of ISS to input-to-output stability. Proc. AACC American Control Conf., Virginia (2001), 2279-2284.
12. B. Ingalls, E. D. Sontag, and Y. Wang, An infinite-time relaxation theorem for differential inclusions. Proc. Amer. Math. Soc. 131 (2002), 487-499.
13. A. Isidori, Nonlinear Control Systems. Springer-Verlag, London (1995).
14. V. Lakshmikantham, S. Lella, and A. A. Martyuk, Practical Stability of Nonlinear Systems. World Scientific, New Jersey (1990).
15. E. D. Sontag and Y. Wang, New characterizations of the input to state stability property. IEEE Trans. Automat. Control 41 (1996), 1283-1294.
16. A. R. Teel and L. Praly, A smooth Lyapunov function from a class-KL estimate involving two positive semi-definite functions. ESAIM Control Optim. Calc. Var. 5 (2000), 313-368.
17. V. I. Vorotnikov, Stability and stabilization of motion: Research approaches, results, distinctive characteristics. Automat. Remote Control 54 (1993), 339-397.
18. J. Warga, Optimal Control of Differential and Functional Equations. Academic Press, New York (1972).