Nonlinear norm-observability notions and stability of switched systems
Hespanha, J.P.
Liberzon, D.
Angeli, D.
Sontag, E.D.
Dept. of Electr. & Comput. Eng., Univ. of California, Santa Barbara, CA, USA;
This paper appears in: Automatic Control, IEEE Transactions on
Publication Date: Feb. 2005
Volume: 50,
Issue: 2
On page(s): 154- 168
ISSN: 0018-9286
INSPEC Accession Number: 8285285
Digital Object Identifier: 10.1109/TAC.2004.841937
Current Version Published: 2005-02-14
Abstract
This work proposes several definitions of "norm-observability" for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for norm-observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems.
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