Nonlinear norm-observability notions and stability of switched systems

João P. Hespanha; Daniel Liberzon; David Angeli; Eduardo D. Sontag

doi:10.1109/TAC.2004.841937

Nonlinear norm-observability notions and stability of switched systems

João P. Hespanha, Daniel Liberzon, David Angeli, Eduardo D. Sontag

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	154-168
Number of pages	15
Journal	IEEE Transactions on Automatic Control
Volume	50
Issue number	2
DOIs	https://doi.org/10.1109/TAC.2004.841937
State	Published - Feb 2005

Keywords

LaSalle's stability theorem
Nonlinear system
Observability
Switched system

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Online availability

10.1109/TAC.2004.841937

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title = "Nonlinear norm-observability notions and stability of switched systems",

abstract = "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.",

keywords = "LaSalle's stability theorem, Nonlinear system, Observability, Switched system",

author = "Hespanha, {Jo{\~a}o P.} and Daniel Liberzon and David Angeli and Sontag, {Eduardo D.}",

note = "Funding Information: Manuscript received July 8, 2003; revised June 8, 2004 and September 30, 2004. Recommended by Associate Editor A. Bemporad. The work of J. P. Hes-panha was supported by the National Science Foundation under Grant ECS-0242798 and by the Army Research Office under Grant DAAD19-03-1-0144. The work of D. Liberzon was supported by the National Science Foundation under Grants NSF ECS-0134115 CAR and NSF ECS-0114725, and by the Defense Advanced Research Projects Agency/Air Force Office of Scientific Research under Grant MURI F49620-02-1-0325. The work of E. D. Sontag was supported by the U.S. Air Force under Grant F49620-01-1-0063 and by the National Science Foundation under Grant CCR-0206789.",

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AU - Hespanha, João P.

AU - Liberzon, Daniel

AU - Angeli, David

AU - Sontag, Eduardo D.

N1 - Funding Information: Manuscript received July 8, 2003; revised June 8, 2004 and September 30, 2004. Recommended by Associate Editor A. Bemporad. The work of J. P. Hes-panha was supported by the National Science Foundation under Grant ECS-0242798 and by the Army Research Office under Grant DAAD19-03-1-0144. The work of D. Liberzon was supported by the National Science Foundation under Grants NSF ECS-0134115 CAR and NSF ECS-0114725, and by the Defense Advanced Research Projects Agency/Air Force Office of Scientific Research under Grant MURI F49620-02-1-0325. The work of E. D. Sontag was supported by the U.S. Air Force under Grant F49620-01-1-0063 and by the National Science Foundation under Grant CCR-0206789.

PY - 2005/2

Y1 - 2005/2

N2 - 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.

AB - 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.

KW - LaSalle's stability theorem

KW - Nonlinear system

KW - Observability

KW - Switched system

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Nonlinear norm-observability notions and stability of switched systems

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