Set-valued Lyapunov functions for difference inclusions

Automatica

Volumn 47, Issue 1, 2011, Pages 127-132

  Goebel, Rafal ^a  

^a LOYOLA UNIVERSITY CHICAGO   (United States)

Author keywords

Asymptotic stability; Consensus; Continuum of equilibria; Converse Lyapunov result; Difference inclusion; Set valued Lyapunov function

Indexed keywords

ASYMPTOTICALLY STABLE; CLOSED SET; CONSENSUS; CONTINUUM OF EQUILIBRIA; DIFFERENCE INCLUSION; INVARIANCE PRINCIPLE; LYAPUNOV; POINTWISE ASYMPTOTIC STABILITY;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; INCLUSIONS;

LYAPUNOV FUNCTIONS;

EID: 78650810636     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2010.10.018     Document Type: Article

References (10)

1. D. Angeli, and P.A. Bliman Stability of leaderless discrete-time multi-agent systems Mathematics of Control, Signals, and Systems 18 2006 293 322
2. S. Bhat, and D. Bernstein Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria SIAM Journal on Control and Optimization 42 2003 1745 1775
3. C. Cai, A. Teel, and R. Goebel Smooth Lyapunov functions for hybrid systems. Part II: (pre-)asymptotically stable compact sets IEEE Transactions on Automatic Control 53 2008 734 748
4. Q. Hui, W. Haddad, and S. Bhat Finite-time semistability and consensus for nonlinear dynamical networks IEEE Transactions on Automatic Control 53 2008 1887 1900
5. Q. Hui, W. Haddad, and S. Bhat Semistability, finite-time stability, differential inclusions, and discontinuous dynamical systems having a continuum of equilibria IEEE Transactions on Automatic Control 54 2009 2465 2470
6. C. Kellett, and A. Teel On the robustness of KL-stability for difference inclusions: smooth discrete-time Lyapunov functions SIAM Journal on Control and Optimization 44 2005 777 800
7. J. Lorenz, and D.A. Lorenz On conditions for convergence to consensus IEEE Transactions on Automatic Control 55 2010 1651 1656
8. L. Moreau Stability of multiagent systems with time-dependent communication links IEEE Transactions on Automatic Control 50 2005 169 182
9. R. Rockafellar, and R.J.B. Wets Variational analysis 1998 Springer
10. E. Sontag Comments on integral variants of ISS Systems and Control Letters 34 1998 93 100