Further input-to-state stability subtleties for discrete-time systems

IEEE Transactions on Automatic Control

Volumn 58, Issue 6, 2013, Pages 1609-1613

  Lazar, Mircea ^a   Heemels, W P Maurice H ^a   Teel, Andy R ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b Santa Barbara   (United States)

Author keywords

Discontinuous systems; discrete time; input to state stability; Lyapunov methods

Indexed keywords

COMPACT SETS; DISCONTINUOUS SYSTEMS; DISCRETE TIME SYSTEM; DISCRETE-TIME; INPUT-TO-STATE STABILITY; TECHNICAL NOTES;

DIGITAL CONTROL SYSTEMS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 84878315618     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2012.2231611     Document Type: Article

References (15)

1. G. Grimm, M. J. Messina, S. E. Tuna, and A. R. Teel, "Examples when nonlinear model predictive control is nonrobust," Automatica, vol. 40, no. 10, pp. 1729-1738, 2004.
2. M. Lazar, W. P. M. H. Heemels, and A. R. Teel, "Lyapunov functions, stability and input-to-state stability subtleties for discrete-time discontinuous systems," IEEE Trans. Autom. Control, vol. 54, no. 10, pp. 2421-2425, Oct. 2009.
3. Z.-P. Jiang and Y. Wang, "Input-to-state stability for discrete-time nonlinear systems," Automatica, vol. 37, pp. 857-869, 2001. (Pubitemid 32426067)
4. R. A. Freeman and P. V. Kokotović, Robust Nonlinear Control Design. Boston, MA: Birkäuser, 2008, reprint of the 1996 edition.
5. M. J. Messina, S. E. Tuna, and A. R. Teel, "Discrete-time certainty equivalence output feedback: Allowing discontinuous control laws including those from model predictive control," Automatica, vol. 41, pp. 617-628, 2005. (Pubitemid 40266208)
6. D. Limon, T. Alamo, F. Salas, and E. F. Camacho, "Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties," Automatica, vol. 42, pp. 797-803, 2006.
7. L. Magni, D. M. Raimondo, and R. Scattolini, "Regional input-to-state stability for nonlinear model predictive control," IEEE Trans. Autom. Control, vol. 51, no. 9, pp. 1548-1553, Sep. 2006. (Pubitemid 44445244)
8. M. Lazar, D. Muñoz de la Peña, W. P. M. H. Heemels, and T. Alamo, "On input-to-state stability of min-max nonlinear model predictive control," Syst. & Control Lett., vol. 57, pp. 39-48, 2008. (Pubitemid 350087248)
9. M. Lazar and W. P. M. H. Heemels, "Predictive control of hybrid systems: Input-to-state stability results for sub-optimal solutions," Auto-matica, vol. 45, no. 1, pp. 180-185, 2009.
10. A. Angeli, E. D. Sontag, and Y. Wang, "A characterization of integral input-to-state stability," IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1082-1097, 2000.
11. B. J. P. Roset, W. P. M. H. Heemels, M. Lazar, and H. Nijmeijer, "On robustness of constrained discrete-time systems to state measurement errors," Automatica, vol. 44, no. 4, pp. 1161-1165, 2008.
12. M. Lazar, W. P. M. H. Heemels, S. Weiland, and A. Bemporad, "Stabilizing model predictive control of hybrid systems," IEEE Trans. Autom. Control, vol. 51, no. 11, pp. 1813-1818, Nov. 2006. (Pubitemid 44824367)
13. G. Pannocchia, J. B. Rawlings, and S. J. Wright, "Conditions under which suboptimal nonlinear MPC is inherently robust," Syst. & Control Lett., vol. 60, no. 9, pp. 747-755, 2011.
14. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory. Cambridge, U.K.: Cambridge University Press, 1993.
15. A. P. Molchanov and E. S. Pyatnitskii, "Criteria of asymptotic stability of differential and difference inclusions encountered in control theory," Syst. & Control Lett., vol. 13, pp. 59-64, 1989.