A smooth Lyapunov function from a class- ${\mathcal{KL}}$ estimate involving two positive semidefinite functions

By Andrew R. Teel, Laurent Praly. 2000

256 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/fcf2ccfbcac8966a2cbdd726e7c224dda19c3824

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In Control and Systems Engineering

Citations in the corpus

Classical Converse Theorems in Lyapunov's Second Method (2015, methodology): “Converse theorems for both strong and weak stability with respect to two measures for both differential and difference inclusions were provided by Teel and Praly [110] and by the author and Teel in [45], [46], [47], and [48].”
Review on computational methods for Lyapunov functions (2015, methodology): “For converse theorems, establishing the existence of Lyapunov functions, see for example Krasovski˘i 1963 [139], Yoshizawa 1966 [228], Hahn 1967 [112], Lin, Sontag and Wang 1996 [152], Teel and Praly 2000 [220] as well as the review in this volume Kellett 2015 [132].”
Passivity as a Design Tool for Group Coordination (2007, methodology): “† Following [ 13 ], we use the notation ´ ! @G1 to indicate a sequence of points ´ in G converging”
Adaptive maneuvering, with experiments, for a model ship in a marine control laboratory (2005, background): “However, as shown by Teel and Praly (2000), a time-varying case can be subsumed into a time-invariant framework by treating time as an additional state with its own dynamics.”
Hybrid systems: Generalized solutions and robust stability (2004, background): “See, for example, ( Teel and Praly, 2000 ) in continuous time and (Kellett and Teel, 2004), (Kellett, 2002) in discrete time.”
Solutions to hybrid inclusions via set and graphical convergence with stability theory applications (2006, methodology): “A particular kind of perturbations appears in converse Lyapunov theory for difierential and difierence inclusion, see [8], [ 32 ], [14].”