Finite-time stabilization of nonlinear impulsive dynamical systems

Nonlinear Analysis: Hybrid Systems

Volumn 2, Issue 3, 2008, Pages 832-845

  Nersesov, Sergey G ^a   Haddad, Wassim M ^b  

^a Villanova University   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

Control Lyapunov functions; Finite time convergence; Finite time stability; Finite time stabilization; Impulsive systems; Non Lipschitzian dynamics; Zeno solutions

Indexed keywords

CONTINUOUS-TIME DYNAMICAL SYSTEMS; CONVERGENCE (MATHEMATICS); ELSEVIER (CO); EQUILIBRIUM STATES; FINITE TIME; FINITE TIME STABILITY (FTS); FINITE TIME STABILIZATION; IMPULSIVE DYNAMICAL SYSTEMS; LIPSCHITZIAN; LYAPUNOV; NON-UNIQUENESS; NUMERICAL EXAMPLES; STABILIZING CONTROLLERS; STABLE EQUILIBRIUM STATE; SUFFICIENT CONDITIONS (SC); SYSTEM DYNAMICS (SD); SYSTEM SOLUTIONS; SYSTEM STATES; VECTOR LYAPUNOV FUNCTIONS;

ARCHITECTURAL DESIGN; COMPUTER NETWORKS; CONTINUOUS TIME SYSTEMS; DIFFERENTIAL EQUATIONS; DYNAMICS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; MECHANICS; NUMERICAL METHODS; STABILIZATION; SYSTEM STABILITY; TELECOMMUNICATION NETWORKS; TRAJECTORIES; UNMANNED AERIAL VEHICLES (UAV);

DYNAMICAL SYSTEMS;

EID: 45449104036     PISSN: 1751570X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nahs.2007.12.001     Document Type: Article

References (28)

1. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
2. Bainov D.D., and Simeonov P.S. Systems with Impulse Effect: Stability, Theory and Applications (1989), Ellis Horwood Limited, England
3. Hu S., Lakshmikantham V., and Leela S. Impulsive differential systems and the pulse phenomena. J. Math. Anal. Appl. 137 (1989) 605-612
4. Bainov D.D., and Simeonov P.S. Impulsive Differential Equations: Asymptotic Properties of the Solutions (1995), World Scientific, Singapore
5. Samoilenko A.M., and Perestyuk N.A. Impulsive Differential Equations (1995), World Scientific, Singapore
6. Haddad W.M., Chellaboina V., and Nersesov S.G. Impulsive and Hybrid Dynamical Systems. Stability, Dissipativity, and Control (2006), Princeton University Press, Princeton, NJ
7. Bupp R.T., Bernstein D.S., Chellaboina V., and Haddad W.M. Resetting virtual absorbers for vibration control. J. Vibr. Contr. 6 (2000) 61-83
8. Haddad W.M., Chellaboina V., and Kablar N.A. Nonlinear impulsive dynamical systems. Part I: Stability and dissipativity. Int. J. Contr. 74 (2001) 1631-1658
9. Haddad W.M., Chellaboina V., and Kablar N.A. Nonlinear impulsive dynamical systems. Part II: Stability of feedback interconnections and optimality. Int. J. Contr. 74 (2001) 1659-1677
10. Haimo V.T. Finite-time controllers. SIAM J. Control Optim. 24 (1986) 760-770
11. Bhat S.P., and Bernstein D.S. Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38 3 (2000) 751-766
12. Agarwal R.P., and Lakshmikantham V. Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations (1993), World Scientific, Singapore
13. Filippov A.F. Differential Equations with Discontinuous Right-Hand Sides. Mathematics and its Applications (Soviet Series) (1988), Kluwer Academic Publishers, Dordrecht
14. Kawski M. Stabilization of nonlinear systems in the plane. Systems Control Lett. 12 (1989) 169-175
15. Yoshizawa T. Stability Theory by Liapunov's Second Method (1966), The Mathematical Society of Japan
16. Bhat S.P., and Bernstein D.S. Geometric homogeneity with applications to finite-time stability. Math. Control Signals Systems 17 (2005) 101-127
17. Bernstein D.S. Matrix Mathematics (2005), Princeton University Press, Princeton, NJ
18. Šiljak D.D. Large-Scale Dynamic Systems: Stability and Structure (1978), Elsevier North-Holland Inc., New York, NY
19. Kamke E. Zur Theorie der Systeme gewöhnlicher Differential-Gleichungen. II. Acta Mathematica 58 (1931) 57-85
20. Wažewski T. Systèmes des équations et des inégalités différentielles ordinaires aux deuxiémes membres monotones et leurs applications. Annales de la Société Polonaise de Mathématique 23 (1950) 112-166
21. Lakshmikantham V., Matrosov V.M., and Sivasundaram S. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems (1991), Kluwer Academic Publishers, Dordrecht, Netherlands
22. Hahn W. Stability of Motion (1967), Springer Verlag, Berlin
23. Haddad W.M., Chellaboina V., and Nersesov S.G. Hybrid nonnegative and compartmental dynamical systems. J. Math. Prob. Eng. 8 (2002) 493-515
24. Haddad W.M., and Chellaboina V. Stability and dissipativity theory for nonnegative dynamical systems: A unified analysis framework for biological and physiological systems. Nonlinear Anal. RWA 6 (2005) 35-65
25. Nersesov S.G., and Haddad W.M. Control vector Lyapunov functions for large-scale impulsive dynamical systems. Nonlinear Anal. Hybrid Syst. 1 (2007) 223-243
26. Nersesov S.G., and Haddad W.M. On the stability and control of nonlinear dynamical systems via vector Lyapunov functions. IEEE Trans. Automat. Control 51 2 (2006) 203-215
27. Haddad W.M., Chellaboina V., and Nersesov S.G. Thermodynamics. A Dynamical Systems Approach (2005), Princeton University Press, Princeton, NJ
28. Nešić D., Mareels I.M.Y., Bastin G., and Mahony R. Output deadbeat control for a class of planar polynomial systems. SIAM J. Control Optim. 36 1 (1998) 253-272