TY - JOUR
T1 - Lyapunov conditions for input-to-state stability of impulsive systems
AU - Hespanha, João P.
AU - Liberzon, Daniel
AU - Teel, Andrew R.
N1 - Funding Information:
João P. Hespanha was born in Coimbra, Portugal, in 1968. He received the Licenciatura in Electrical and Computer Engineering from the Instituto Superior Técnico, Lisbon, Portugal in 1991 and the Ph.D. degree in Electrical Engineering and Applied Science from Yale University, New Haven, Connecticut in 1998. He currently holds a Professor position with the Department of Electrical and Computer Engineering, the University of California, Santa Barbara. From 1999 to 2001, he was an Assistant Professor at the University of Southern California, Los Angeles. His research interests include hybrid and switched systems; the modeling and control of communication networks; distributed control over communication networks (also known as networked control systems); the use of vision in feedback control; and stochastic modeling in biology. Dr. Hespanha is the recipient of the Yale University’s Henry Prentiss Becton Graduate Prize for exceptional achievement in research in Engineering and Applied Science, a National Science Foundation CAREER Award, the 2005 best paper award at the 2nd Int. Conf. on Intelligent Sensing and Information Processing, the 2005 Automatica Theory/Methodology best paper prize, and the 2006 George S. Axelby Outstanding Paper Award. Dr. Hespanha is a Fellow of the IEEE and an IEEE distinguished lecturer since 2007.
Funding Information:
J. Hespanha supported by the NSF grant No. CNS-0720842 and the ARO grant DAAD19-03-1-0144. A. Teel supported by the grant NSF ECS-0622253 and the AFOSR grant F9550-06-1-0134. D. Liberzon supported by the NSF grant ECS-0134115 CAR and the DARPA/AFOSR MURI grant F49620-02-1-0325. This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Zongli Lin under the direction of Editor Hassan K. Khalil.
PY - 2008/11
Y1 - 2008/11
N2 - This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for impulsive systems, i.e., dynamical systems that evolve according to ordinary differential equations most of the time, but occasionally exhibit discontinuities (or impulses). We provide a set of Lyapunov-based sufficient conditions for establishing these ISS properties. When the continuous dynamics are ISS, but the discrete dynamics that govern the impulses are not, the impulses should not occur too frequently, which is formalized in terms of an average dwell-time (ADT) condition. Conversely, when the impulse dynamics are ISS, but the continuous dynamics are not, there must not be overly long intervals between impulses, which is formalized in terms of a novel reverse ADT condition. We also investigate the cases where (i) both the continuous and discrete dynamics are ISS, and (ii) one of these is ISS and the other only marginally stable for the zero input, while sharing a common Lyapunov function. In the former case, we obtain a stronger notion of ISS, for which a necessary and sufficient Lyapunov characterization is available. The use of the tools developed herein is illustrated through examples from a Micro-Electro-Mechanical System (MEMS) oscillator and a problem of remote estimation over a communication network.
AB - This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for impulsive systems, i.e., dynamical systems that evolve according to ordinary differential equations most of the time, but occasionally exhibit discontinuities (or impulses). We provide a set of Lyapunov-based sufficient conditions for establishing these ISS properties. When the continuous dynamics are ISS, but the discrete dynamics that govern the impulses are not, the impulses should not occur too frequently, which is formalized in terms of an average dwell-time (ADT) condition. Conversely, when the impulse dynamics are ISS, but the continuous dynamics are not, there must not be overly long intervals between impulses, which is formalized in terms of a novel reverse ADT condition. We also investigate the cases where (i) both the continuous and discrete dynamics are ISS, and (ii) one of these is ISS and the other only marginally stable for the zero input, while sharing a common Lyapunov function. In the former case, we obtain a stronger notion of ISS, for which a necessary and sufficient Lyapunov characterization is available. The use of the tools developed herein is illustrated through examples from a Micro-Electro-Mechanical System (MEMS) oscillator and a problem of remote estimation over a communication network.
KW - Impulsive systems
KW - Input-to-state stability
KW - Nonlinear systems
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U2 - 10.1016/j.automatica.2008.03.021
DO - 10.1016/j.automatica.2008.03.021
M3 - Article
AN - SCOPUS:55049084001
SN - 0005-1098
VL - 44
SP - 2735
EP - 2744
JO - Automatica
JF - Automatica
IS - 11
ER -