Convergent piecewise affine systems: Analysis and design Part I: continuous case

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 5391-5396

  Pavlov, Alexey ^a   Van De Wouw, Nathan ^b   Nijmeijer, Henk ^b  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FEEDBACK CONTROL; LYAPUNOV METHODS; TRACKING (POSITION);

INPUT TO STATE CONVERGENCE; PIECEWISE AFFINE (PWA) SYSTEMS; PWA CONTROL SYSTEMS; SYSTEM DYNAMICS;

CONTROL SYSTEM ANALYSIS;

EID: 33847194991     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1583019     Document Type: Conference Paper

References (23)

1. A. Pogromsky, "Passivity based design of synchronizing systems," In. J. Bifurcation Chaos, vol. 8(2), pp. 295-319, 1998.
2. A. Juloski, M. Heemels, and S. Weiland, "Observer design for a class of piecewise affine systems," in Proc. of IEEE Conf. Decision and Control, 2002.
3. A. Pavlov, N. van de Wouw, and H. Nijmeijer, "The uniform global output regulation problem," in Proc. of IEEE Conf. Decision and Control, 2004.
4. A. Pavlov, "The output regulation problem: a convergent dynamics approach," Ph.D. dissertation, Eindhoven University of Technology, Eindhoven, 2004.
5. M. Heertjes and M. Steinbuch, "Stability and performance of variable gain controllers with application to a DVD storage drive," Automation, vol. 40, pp. 591-602, 2004.
6. V. Pliss, Nonlocal problems of the theory of oscillations. London: Academic Press, 1966.
7. B. Demidovich, Lectures on stability theory (in Russian), Moscow: Nauka, 1967.
8. A. Pavlov, A. Pogromsky, N. van de Wouw, and H. Nijmeijer, "Convergent dynamics, a tribute to Boris Pavlovich Demidovich," Systems and Control Letters, vol. 52, pp. 257-261, 2004.
9. V. Yakubovich, "Matrix inequalities method in stability theory for nonlinear control systems: I. absolute stability of forced vibrations," Automation and Remote Control, vol. 7, pp. 905-917, 1964.
10. J. LaSalle and S. Lefschetz, Stability by Liapunov's direct method with applications. New York: Academic press, 1961.
11. T. Yoshizawa, Stability theory by Liapunov's second method. Tokio: The Mathematical Society of Japan, 1966.
12. D. Angeli, "A Lyapunov approach to incremental stability properties," IEEE Trans. Automatic Control, vol. 47, pp. 410-421, 2002.
13. V. Fromion, G. Scorletti, and G. Ferreres, "Nonlinear performance of a PI controlled missile: an explanation," Int. J. Robust Nonlinear Control, vol. 9, pp. 485-518, 1999.
14. W. Lohmiller and J.-J. Slotine, "On contraction analysis for nonlinear systems," Automatica, vol. 34, pp. 683-696, 1998.
15. M. Johansson and A. Rantzer, "Computation of piecewise quadratic lyapunov functions for hybrid systems," IEEE Trans. Automatic Control, vol. 43, pp. 555-559, 1998.
16. W. Heemels, M. Camlibel, and J. Schumacher, "On the dynamic analysis of piecewise-linear networks," IEEE Trans. Circuits and Systems I: Fundamental Theory and Applications, vol. 49, pp. 315-327, 2002.
17. A. Bemporad, G. Ferrari-Trecate, and M. Morari, "Observability and controllability of piecewise affine and hybrid systems," IEEE Trans. Automatic Control, vol. 45, pp. 1864-1876, 2000.
18. D. Liberzon, Switchings in systems and control. Boston: Birkhauser, 2003.
19. A. Pavlov, A. Pogromsky, N. van de Wouw, and H. Nijmeijer, "Convergent piecewise affine systems: analysis and design. Part II: discontinuous case." in Proc. of IEEE Conf. Decision and Control, 2005.
20. A. Pavlov, N. van de Wouw, and H. Nijmeijer, "Convergent systems: analysis and design," in Symposium on Nonlinear Controller and Observer Design - From Theoiy to Applications, 2005.
21. B. Demidovich, "Dissipativity of a nonlinear system of differential equations, parti," Vestnik Moscow State Univiersity, set: matem. mekh., (in Russian), vol. 6, pp. 19-27, 1961.
22. H. Khalil, Nonlinear systems, 2nd ed. Upper Saddle River: Prentice Hall, 1996.
23. A. Pavlov, N. van de Wouw, and H. Nijmeijer, "The global output regulation problem: an incremental stability approach," in Proc. of 6th IFAC Symposium on Nonlinear Control Systems, 2004.