Vector dissipativity theory for large-scale impulsive dynamical systems

Mathematical Problems in Engineering

Volumn 2004, Issue 3, 2004, Pages 225-267

  Haddad, Wassim M ^a   Chellaboina, Vijaysekhar ^b   Hui, Qing ^a   Nersesov, Sergey ^a  

^a Georgia Institute of Technology   (United States)

^b UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; FEEDBACK CONTROL; FUNCTIONS; HIERARCHICAL SYSTEMS; LYAPUNOV METHODS; VECTORS;

CONTROLLER ANALYSIS; IMPULSIVE SYSTEMS INTERCONNECTIONS; LARGE-SCALE DYNAMICAL SYSTEMS; VECTOR DISSIPATIVE THEORY;

LARGE SCALE SYSTEMS;

EID: 10844237905     PISSN: 1024123X     EISSN: None     Source Type: Journal    
DOI: 10.1155/S1024123X04310021     Document Type: Article

References (28)

1. P. J. Antsaklis and A. Nerode (eds.), Special issue on hybrid control systems, IEEE Trans. Automat. Control 43 (1998), no. 4.
2. R. Bellman, Vector Lyapunov functions, J. SIAM Control 1 (1962), 32-34.
3. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press (Harcourt Brace Jovanovich Publishers), New York, 1979.
4. D. S. Bernstein and S. P. Bhat, Nonnegativity, reducibility and semistability of mass action kinetics, Proc. IEEE Conference on Decision and Control (Ariz, 1999), December 1999, pp. 2206-2211.
5. D. S. Bernstein and D. C. Hyland, Compartmental modeling and second-moment analysis of state space systems, SIAM J. Matrix Anal. Appl. 14 (1993), no. 3, 880-901.
6. S. Boyd, L. El. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, vol. 15, Society for Industrial and Applied Mathematics (SIAM), Pennsylvania, 1994.
7. Lj. T. Grujić, A. A. Martynyuk, and M. Ribbens-Pavella, Large Scale Systems Stability under Structural and Singular Perturbations, Lecture Notes in Control and Information Sciences, vol. 92, Springer-Verlag, Berlin, 1987.
8. W. M. Haddad and V. Chellaboina, Dissipativity theory and stability of feedback interconnections for hybrid dynamical systems, Math. Probl. Eng. 7 (2001), no. 4, 299-335.
9. W. M. Haddad, V. Chellaboina, and E. August, Stability and dissipativity theory for nonnegative dynamical systems: a thermodynamic framework for biological and physiological systems, Proc. IEEE Conference on Decision and Control (Fla, 2001), December 2001, pp. 442-458.
10. W. M. Haddad, V. Chellaboina, and N. A. Kablar, Non-linear impulsive dynamical systems. I. Stability and dissipativity, Internat. J. Control 74 (2001), no. 17, 1631-1658.
11. _, Non-linear impulsive dynamical systems. II. Stability of feedback interconnections and optimality, Internat. J. Control 74 (2001), no. 17, 1659-1677.
12. W. M. Haddad, V. Chellaboina, and S. G. Nersesov, Large-scale nonlinear dynamical systems: a vector dissipative systems approach, Proc. IEEE Conference on Decision and Control (Hawaii, 2003), December 2003, pp. 5603-5608.
13. _, Thermodynamics and large-scale nonlinear dynamical systems: a vector dissipative systems approach, Dynam. Contin. Discrete Impuls. Systems 11 (2004), 609-649.
14. D. J. Hill and P. J. Moylan, Stability results for nonlinear feedback systems, Automatica J. IFAC 13 (1977), no. 4, 377-382.
15. V. Lakshmikantham, D. D. Baǐnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics, vol. 6, World Scientific Publishing, New Jersey, 1989.
16. V. Lakshmikantham, V. M. Matrosov, and S. Sivasundaram, Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems, Mathematics and Its Applications, vol. 63, Kluwer Academic Publishers, Dordrecht, 1991.
17. J. Lunze, Stability analysis of large-scale systems composed of strongly coupled similar subsystems, Automatica J. IFAC 25 (1989), no. 4, 561-570.
18. A. A. Martynyuk, Stability of Motion of Complex Systems, Izdat. Naukova Dumka, Kiev, 1975.
19. _, Stability by Liapunov's Matrix Function Method with Applications, Monographs and Textbooks in Pure and Applied Mathematics, vol. 214, Marcel Dekker, New York, 1998.
20. _, Qualitative Methods in Nonlinear Dynamics. Novel Approaches to Liapunov's Matrix Functions, Monographs and Textbooks in Pure and Applied Mathematics, vol. 246, Marcel Dekker, New York, 2002.
21. V. M. Matrosov, Method of Lyapunov-vector functions in feedback systems, Avtomat. i Telemeh. (1972), no. 9, 63-75 (Russian).
22. A. N. Michel and B. Hu, Towards a stability theory of general hybrid dynamical systems, Automatica J. IFAC 35 (1999), no. 3, 371-384.
23. A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems, Academic Press (Harcourt Brace Jovanovich Publishers), New York, 1977.
24. A. N. Michel, K. Wang, and B. Hu, Qualitative Theory of Dynamical Systems. The Role of Stability Preserving Mappings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 239, Marcel Dekker, New York, 2001.
25. A. S. Morse, C. C. Pantelides, S. Sastry, and J. M. Schumacher (eds.), Special issue on hybrid control systems, Automatica J. IFAC 35 (1999), no. 3.
26. D. D. Šiljak, Large-Scale Dynamic Systems. Stability and Structure, North-Holland Series in System Science and Engineering, vol. 3, North-Holland, New York, 1979.
27. _, Complex dynamic systems: dimensionality, structure, and uncertainty, Large Scale Systems 4 (1983), 279-294.
28. H. Ye, A. N. Michel, and L. Hou, Stability theory for hybrid dynamical systems, IEEE Trans. Automat. Control 43 (1998), no. 4, 461-474.