Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 50, Issue 2, Pages 154-168Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2004.841937
Keywords
LaSalle's stability theorem; nonlinear system; observability; switched system
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This paper 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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