Parametrization of piecewise linear Lyapunov functions via linear programming

International Journal of Control

Volumn 72, Issue 7, 1999, Pages 702-715

  Julián, Pedro ^a   Guivant, José ^a   Desages, Alfredo ^a,b  

^a UNIVERSIDAD NACIONAL DEL SUR   (Argentina)

^b Centro Científico y Tecnológico Consejo Nacional de Investigaciones Científicas y Técnicas   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR PROGRAMMING; NONLINEAR CONTROL SYSTEMS; PIECEWISE LINEAR TECHNIQUES; SYSTEM STABILITY; SYSTEMS ANALYSIS; UNCERTAIN SYSTEMS;

PARAMETRIZATION; STABILITY ANALYSIS;

LYAPUNOV METHODS;

EID: 0032632143     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/002071799220876     Document Type: Article

References (37)

1. ANDERSEN, E., GONDZIO, J., MÉSZÁROS, C., and XU, X. 1996, Implementation of interior point methods for large scale linear programming. Technical Report 1996.3 (Geneva: Logilab, University of Geneva).
2. APOSTOL, T., 1957, Mathematical Analysis (AddisonWesley).
3. BLANCHINI, F., 1995, Nonquadratic Lyapunov functions for robust control. Automatica, 31, 451-461.
4. BRAYTON, R., and TONG, C., 1979, Stability of dynamical systems: A constructive approach. IEEE Transactions on Circuits and Systems, CAS-26, 224-234.
5. BRAYTON, R., and TONG, C., 1980, Constructive stability and asymptotic stability of dynamical systems. IEEE Transactions on Circuits and Systems, CAS-27, 1121-1130.
6. CHIANG, H., and THORP, J., 1989, Stability regions of non-linear dynamical systems: A constructive methodology. IEEE Transactions on Automatic Control, AC-34, 1229-1241.
7. CHIEN, M., and KUH, E., 1977, Solving non-linear resistive networks using piecewise-linear analysis and simplicial subdivision. IEEE Transactions on Circuits and Systems, CAS-24, 305-317.
8. CHUA, L. O., and DENG, A., 1986, Canonical piecewise-linear modeling. IEEE Transactions on Circuits and Systems, CAS-33, 511-525.
9. CHUA, L. O., and YING, R., 1983, Canonical piecewise-linear analysis. IEEE Transactions on Circuits and Systems, CAS-30, 125-140.
10. DESAGES, A., COLANTONIO, C., and CHEN, G., 1996, Matching conditions for stability analysis of non-linear feedback control systems. Mathematical Computer Modelling, 23, 1-10.
11. GONDZIO, J., 1995, HOPDM (version 2.12) - a fast 1P solver based on a primal-dual interior point method. European Journal of Operational Research, 85, 221-225.
12. HAHN, W., 1967, Stability of Motion (Springer Verlag).
13. JULIÁN, P., JORDÁN, M., and DESAGES, A., 1998, Canonical piecewise linear approximations of smooth functions. IEEE Transactions on Circuits and Systems, 45, 567-579.
14. JULIÁN, P., DESAGES, A., and AGAMENNONI, O., 1997, High level canonical piecewise linear representation using simplicial subdivision, IEEE Transactions on Circuits and Systems, (to appear).
15. JULIÁN, P., DESAGES, A., and AGAMENNONI, O., 1998, On the high level representation of canonical piecewise linear functions. ISCAS'98, Monterey, CA.
16. KAHLERT, C., and CHUA, L. O., 1992, The complete canonical piecewise-linear representation - Part I: The geometry of the domain space. IEEE Transactions on Circuits and Systems, 39, 222-236.
17. KHALIL, H., 1992, Non-linear Systems (London: Macmillan).
18. KIENDL, H., and RUGER, J. J., 1995, Stability analysis of fuzzy control systems using facet functions. Fuzzy Sets and Systems, 70, 275-285.
19. KIENDL, H., ADAMY, J., and STELZNER, P., 1992, Vector norms as Lyapunov functions for linear systems. IEEE Transactions on Automatical Control, AC-37, 839-842.
20. LIN, J. N., and UNBEHAUEN, R., 1990, Adaptive non-linear digital filter with canonical piecewise-linear function structure. IEEE Transactions on Circuits and Systems, 37, 347-353.
21. LIN, J. N., XU, H., and UNBEHAUEN, R., 1994, A generalization of canonical piecewise-linear functions. IEEE Transactions on Circuits and Systems, 41, 345-347.
22. LUSTIG, I., and ROTHBERG, E., 1996, Gigaflops in linear programming. Operational Research Letters, 18, 157-165.
23. LUSTIG, I., MARSTEN, R., and SHANNO, D., 1994, Interior point methods for linear programming: Computational state of the art. ORSA Journal on Computing, 6, 1-14.
24. MICHEL, A., NAM, B. H., and VITTAL, V., 1984, Computer generated Lyapunov functions for interconnected systems: Improved results with applications to power systems. IEEE Transactions on Circuits and Systems, CAS-31, 189-198.
25. MICHEL, A., SARABUDLA, N., and MILLER, R., 1982, Stability analysis of complex dynamical systems: Some computational methods. Circuits and Systems Signal Processing, 1, 171-202.
26. NEMHAUSER, KAN, and TODD., 1996, Optimization (North-Holland).
27. OHTA, Y., IMANISHI, H., GONG, L., and HANEDA, H., 1993, Computer generated Lyapunov functions for a class of non-linear systems. IEEE Transactions on Circuits and Systems, CAS-40, 343-354.
28. OLAS, A., 1994, Construction of optimal Lyapunov functions for systems with structured uncertainties. IEEE Transactions on Automatic Control, AC-39, 167-171.
29. POLANSKY, A., 1995, On infinity norms as Lyapunov functions for linear systems. IEEE Transactions on Automatic Control, AC-40, 1270-1274.
30. SONTAG, E., 1981, Non-linear regulation: The piecewise linear approach. IEEE Transactions on Automatic Control, AC-26, 346-357.
31. SONTAG, E., 1995, Worst-case identification of non-linear fading memory systems. Automatica, 31.
32. VANDERBEI, R., 1996, Linear Programming: Foundations and Extensions (Kluwer Academic Publishers).
33. VIDYASAGAR, M., 1993, Non-linear Systems Analysis (Englewood Cliffs, NJ: Prentice-Hall).
34. WANG, K., and MICHEL, A., 1996, On the stability of a family of non-linear time-varying systems. IEEE Transactions on Circuits and Systems, CAS-43, 517-531.
35. WEISSENBERGER, S., 1969, Piecewise-quadratic and piecewise-linear Lyapunov functions for discontinuous systems. International Journal of Control, 10, 171-180.
36. YAMAMURA, K., 1992, On piecewise-linear approximation of non-linear mappings containing Gummel-Poon models or Shichman-Hodges models. IEEE Transactions on Circuits and Systems, 39, 694-697.
37. YOSHIZAWA, T., 1966, Stability Theory by Liapunov Second Method (Mathematical Society of Japan).