Conditions for the existence of continuous storage functions for nonlinear dissipative systems

Systems and Control Letters

Volumn 54, Issue 1, 2005, Pages 73-81

  Polushin, I G ^a,b,c   Marquez, H J ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

^b LAKEHEAD UNIVERSITY   (Canada)

^c INSTITUTE OF PROBLEMS OF MECHANICAL ENGINEERING   (Russian Federation)

Author keywords

Dissipative systems; Local w uniform reachability; Nonlinear systems; Storage functions; Weak accessibility

Indexed keywords

CONTROLLABILITY; LYAPUNOV METHODS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; TRAJECTORIES; VIRTUAL STORAGE;

DISSIPATIVE SYSTEMS; LOCAL W-UNIFORM REACHABILITY; STORAGE FUNCTIONS; WEAK ACCESSIBILITY;

NONLINEAR SYSTEMS;

EID: 9644300956     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2004.06.007     Document Type: Article

References (14)

1. F. Clarke, Y. Ledyaev, E. Sontag, A. Subbotin, Asymptotic controllability implies feedback stabilization, IEEE Trans. Automat. Control AC-42 (1997) 1394-1407.
2. R. Hermann, A.J. Krener, Nonlinear controllability and observability, IEEE Trans. Automat, Control AC-22 (1977) 728-740.
3. D.J. Hill, On the relation between input-output and Lyapunov stability results for interconnected systems, in: Proceedings of the 21st Midwest Symposium on Circuits and Systems, Ames, Iowa, 1978.
4. D.J. Hill, P.J. Moylan, Stability of nonlinear dissipative systems, IEEE Trans. Automat. Control AC-21 (1976) 708-711.
5. D.J. Hill, P.J. Moylan, Dissipative dynamical systems: basic input-output and state properties, J. Franklin Inst. 309 (1980) 327-357.
6. M.R. James, A partial differential inequality for dissipative nonlinear systems, Syst. Control Lett. 21 (1993) 315-320.
7. ∞ control, in: Proceedings of the Third IFAC Symposium on Nonlinear Control Systems (NOLCOS 1996), Lake Tahoe, June 1995.
8. R. Lozano, B. Brogliato, O. Egeland, B. Maschke, Dissipative Systems Analysis and Control, Theory and Applications, Springer, Berlin, 2000.
9. H. Njmeijer, A. van der Schaft, Nonlinear Dynamical Control Systems, Springer, New York, 1990.
10. I.G. Polushin, H.J. Marquez, On the existence of a continuous storage function for dissipative systems, Syst. Control Lett. 46 (2) (2002) 85-90.
11. E.D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, second ed., Springer, New York, 1998.
12. E.D. Sontag, The ISS philosophy as a unifying framework for stability-like behaviour, in: A. Isidori, F. Lamnabhi-Lagarrigue, W. Respondek (Eds.), Nonlinear Control in the Year 2000, Lecture Notes in Control and Information Sciences, vol. 2, Springer, Berlin, 2000, pp. 443-468.
13. 2-Gain and Passivity Techniques in Nonlinear Control, Communications and Control Engineering, second ed., Springer, London, 1999.
14. J.C. Willems, Dissipative dynamical systems. Part I: general theory, Arch. Rational Mech. Anal. 45 (5) (1972) 321-351.