Asymptotic stability of piecewise affine systems with sampled-data piecewise linear controllers

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2011, Pages 8315-8320

  Moarref, Miad ^a   Rodrigues, Luis ^a  

^a Dept of Electrical and Computer Engineering   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONTINUOUS TIME SYSTEMS; CONTROLLERS; DELAY CONTROL SYSTEMS; LINEAR CONTROL SYSTEMS; LYAPUNOV FUNCTIONS; PIECEWISE LINEAR TECHNIQUES; SAMPLED DATA CONTROL SYSTEMS; SYSTEM STABILITY; TIME DELAY;

LYAPUNOV-KRASOVSKII FUNCTIONAL (LKF); OPTIMIZATION PROGRAMS; PIECEWISE AFFINE SYSTEMS; PIECEWISE LINEAR CONTROLLERS; SAMPLED DATA SYSTEMS; STABILITY ANALYSIS; TIME DELAY APPROACH; VARIABLE TIME DELAY;

FEEDBACK;

EID: 84860685237     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2011.6160917     Document Type: Conference Paper

References (16)

1. L. Rodrigues and J. How, "Automated control design for a piecewise-affine approximation of a class of nonlinear systems," in Proc. American Control Conference, 2001, pp. 3189-3194.
2. M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 555-559, 1998.
3. A. Hassibi and S. Boyd, "Quadratic stabilization and control of piecewise-linear systems," in Proc. American Control Conference, 1998, pp. 3659-3664.
4. M. Johansson, Piecewise Linear Control Systems. Berlin: Springer, 2003, vol. 6, no. 1.
5. L. Rodrigues, "Stability analysis of piecewise-affine systems using controlled invariant sets," Systems & Control Letters, vol. 53, no. 2, pp. 157-169, 2004.
6. L. Rodrigues and S. Boyd, "Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization," Systems & Control Letters, vol. 54, no. 9, pp. 835-853, 2005.
7. 2-gain control of piecewise affine slab differential inclusions," Automatica, vol. 45, no. 3, pp. 812-816, 2009.
8. D. S. Laila, D. Nešić, and A. R. Teel, "Open and closed loop dissipation inequalities under sampling and controller emulation," European Journal of Control, vol. 8, no. 2, pp. 109-125, 2002.
9. T. Chen and B. Francis, Optimal Sampled-Data Control Systems. Springer-Verlag, 1995.
10. S. Azuma and J. Imura, "Optimal control of sampled-data piecewise affine systems and its application to CPU processing control," in Proc. 42nd IEEE Conference on Decision and Control, 2003, pp. 161-166.
11. J. Imura, "Optimal continuous-time control of sampled-data piecewise affine systems," in Proc. American Control Conference, 2003, pp. 5317-5322.
12. L. Rodrigues, "Stability of sampled-data piecewise-affine systems under state feedback," Automatica, vol. 43, no. 7, pp. 1249-1256, 2007.
13. A. R. Teel, D. Nešić, and P. Kokotovic, "A note on input-to-state stability of sampled-data nonlinear systems," in Proc. 37th IEEE Conference on Decision and Control, 1998, pp. 2473-2478.
14. P. Naghshtabrizi, J. P. Hespanha, and A. R. Teel, "Exponential stability of impulsive systems with application to uncertain sampled-data systems," Systems & Control Letters, vol. 57, no. 5, pp. 378-385, 2008.
15. B. Samadi and L. Rodrigues, "Stability of sampled-data piecewise affine systems: A time-delay approach," Automatica, vol. 45, no. 9, pp. 1995-2001, 2009.
16. J. K. Hale and S. M. V. Lunel, Introduction to functional differential equations. Springer, 1993.