Connective stability of discontinuous dynamic systems

Journal of Optimization Theory and Applications

Volumn 115, Issue 3, 2002, Pages 711-726

  Stipanovic D M ^a   Siljak D D ^b  

^a 496 Lomita Mall   (United States)

^b Santa Clara University   (United States)

Author keywords

Connective stability; discontinuous systems; Filippov solution; M matrices; polytopic uncertainty; vector Lyapunov functions

Indexed keywords

CONVEX OPTIMIZATION; SYSTEM STABILITY;

CONNECTIVE STABILITY; DISCONTINOUS SYSTEMS; FILIPPOV SOLUTIONS; LIPSCHITZ; M-MATRICES; M-MATRIX; POLYTOPIC UNCERTAINTIES; STABILITY CONDITION; STRUCTURAL PERTURBATION; VECTOR LYAPUNOV FUNCTIONS;

LYAPUNOV FUNCTIONS;

EID: 0036441077     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021215500258     Document Type: Article

References (38)

1. ŠILJAK, D. D., Stability of Large-Scale Systems under Structural Perturbations, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 2, pp. 657-663, 1972.
2. ŠILJAK, D. D., Large-Scale Dynamic Systems: Stability and Structure, North-Holland, New York, New York, 1978.
3. FILIPPOV, A. F., Differential Equations with Discontinuous Right-Hand Side, American Mathematical Society Translations, Vol. 42, pp. 199-231, 1964.
4. FILIPPOV, A. F., Differential Equations with Discontinuous Right-Hand Sides, Kluwer, Boston, Massachusetts, 1988.
5. ROXIN, E., Stability in General Control Systems, Journal of Differential Equations, Vol. 1, pp. 115-150, 1965.
6. UTKIN, V. I., Sliding Modes and Their Application in Variable Structure Systems, Mir Publishers (English Translation), Moscow, Russia, 1978.
7. PADEN, B. E., and SASTRY, S. S., A Calculus for Computing Filippov's Differential Inclusion with Application to the Variable Structure Control of Robot Manipulators, IEEE Transactions on Circuits and Systems, Vol. 34, pp. 73-82, 1987.
8. SHEVITZ, D. S., and PADEN, B., Lyapunov Stability Theory of Nonsmooth Systems, IEEE Transactions on Automatic Control, Vol. 39, pp. 1910-1914, 1994.
9. MICHEL, A. N., and PORTER, D. W., Analysis of Discontinuous Large-Scale Systems: Stability, Transient Behavior and Trajectory Bounds, International Journal of System Science, Vol. 2, pp. 77-95, 1971.
10. MICHEL, A. N., and HU, B., Stability Analysis of Interconnected Hybrid Dynamical Systems, Proceedings of the IFAC Symposium on Large Scale Systems, Patras, Greece, pp. 698-703, 1998.
11. RUAN, S., Connective Stability of Discontinuous Large Scale Systems, Journal of Mathematical Analysis and Applications, Vol. 160, pp. 480-484, 1991.
12. BARMISH, B. R., and DEMARCO, C. L., A New Method for Improvement of Robustness Bounds for Linear State Equations, Proceedings of the Conference on Information Sciences and Systems, Princeton, New Jersey, pp. 115-120, 1986.
13. STIPANOVIĆ, D. M., and ŠILJAK, D. D., Convex M-Matrices and Polytopic Dynamic Systems, Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, California, pp. 4366-4368, 1997.
14. CLARKE, F. H., Optimization and Nonsmooth Analysis, Wiley, New York, New York, 1983.
15. CLARKE, F. H., LEDYAEV, YU., S., STERN, R. J., and WOLENSKI, P. R., Non-smooth Analysis and Control Theory, Springer-Verlag, New York, New York, 1998.
16. KHALIL, H. K., Nonlinear Systems, Prentice-Hall, Upper Saddle River, New Jersey, 1996.
17. ŠILJAK, D. D., Connective Stability of Competitive Equilibrium, Automatica, Vol. 11, pp. 389-400, 1975.
18. LAKSHMIKANTHAM, V., MATROSOV, V. M., and SIVASUNDARAM, S., Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems, Kluwer Academic Publishers, Dordrecht, Netherlands, 1991.
19. ŠILJAK, D. D., Decentralized Control of Complex Systems, Academic Press, Boston, Massachusetts, 1991.
20. MARTYNYUK, A. A., Stability of Discrete Systems under Structural Perturbations, International Applied Mechanics, Vol. 33, pp. 329-334, 1997.
21. ŠILJAK, D. D., and STIPANOVIĆ, D. M., Polytopic Connective Stability, Proceedings of the IFAC Symposium on Large Scale Systems, Patras, Greece, pp. 1477-1484, 1998.
22. MARTYNYUK, A. A., and THI, S. C., On the Coherent Practical Motion of Systems with Delay, International Applied Mathematics, Vol. 35, pp. 87-92, 1999.
23. KOBAYASHI, Y., IKEDA, M., and FUJISAKI, Y., Fault-Tolerant Decentralized Control for Large Space Structures, Proceedings of the IEEE International Conference on Control Applications, Kohala Coast, Hawaii, pp. 303-308, 1999.
24. MARTYNYUK, A. A., Stability Analysis of Discrete Systems, International Applied Mathematics, Vol. 36, pp. 835-865, 2000.
25. SATHANANTHAN, S., SUTHHAHARAN, S., and LADDE, G. S., Large Scale Integro-Differential Systems under Structural Perturbations, Communications in Applied Analysis, Vol. 4, pp. 459-474, 2000.
26. MARTYNYUK, A. A., and STAVROULAKIS, I. P., Novel Stability and Instability Conditions for Interconnected Systems with Structural Perturbations, Dynamics of Continuous, Discrete and Impulsive Systems, Vol. 7, pp. 307-324, 2000.
27. STIPANOVIĆ, D. M., and ŠILJAK, D. D., Stability of Polytopic Systems via Convex M-Matrices and Parameter-Dependent Lyapunov Functions, Nonlinear Analysis, Vol. 40, pp. 589-609, 2000.
28. BRANICKY, M. S., Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems, IEEE Transactions on Automatic Control, Vol. 43, pp. 475-482, 1998.
29. BERMAN, A., and PLEMMONS, R. J., Nonnegative Matrices in Mathematical Sciences, Academic Press, New York, New York, 1979.
30. FIEDLER, M., and PTÀK, V., On Matrices with Non-positive Off-Diagonal Elements and Positive Principal Minors, Czechoslovakian Mathematical Journal, Vol. 12, pp. 382-400, 1962.
31. HORN, R. A., and JOHNSON, C. R., Topics in Matrix Analysis, Cambridge University Press, Cambridge, United Kingdom, 1991.
32. FAN, K., Inequalities for the Sum of Two M-Matrices, Inequalities, Edited by O. Shiha, Academic Press, New York, New York, pp. 105-117, 1967.
33. BURGAT, C., and BERNUSSOU, J., On the Stability of Interconnected Systems with Periodic Structural Perturbations, International Journal of System Science, Vol. 9, pp. 1133-1143, 1978.
34. HORISBERGER, H. P., and BÈLANGER, P. R., Regulators for Linear, Time-Invariant Plants with Uncertain Parameter, IEEE Transactions on Automatic Control, Vol. 21, pp. 705-708, 1976.
35. BOYD, S., GHAOUI, L. E., FERON, E., and BALAKRISHNAN, V., Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, Pennsylvania, 1994.
36. BELLMAN, R., Vector Lyapunov Functions, SIAM Journal of Control, Vol. 1, pp. 32-34, 1962.
37. MATROSOV, V. M., On the Theory of Stability of Motion, Prikladnaia Matematika i Mekhanika, Vol. 26, pp. 992-1000, 1962.
38. ARAKI, M., Application of M-Matrices to the Stability Problems of Composite Dynamical Systems, Journal of Mathematical Analysis and Applications, Vol. 52, pp. 309-321, 1975.