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An invariance principle for nonlinear hybrid and impulsive dynamical systems

DSpace at IIT Bombay

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Title An invariance principle for nonlinear hybrid and impulsive dynamical systems
 
Creator CHELLABOINA, VIJAYSEKHAR
BHAT, SP
HADDAD, WASSIM M
 
Subject lyapunov methods
system stability
theorem proving
invariance
 
Description In this paper we develop an invariance principle for dynamical systems possessing left-continuous flows. Specifically, we show that left-continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi-infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems. As a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems; namely, state-dependent impulsive dynamical systems. These results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems.
 
Publisher Elsevier
 
Date 2009-02-21T11:33:47Z
2011-11-25T17:25:29Z
2011-12-26T13:05:56Z
2011-12-27T05:53:50Z
2009-02-21T11:33:47Z
2011-11-25T17:25:29Z
2011-12-26T13:05:56Z
2011-12-27T05:53:50Z
2003
 
Type Article
 
Identifier Nonlinear Analysis 53(3-4), 527-550
0362-546X
http://dx.doi.org/10.1016/S0362-546X(02)00316-4
http://hdl.handle.net/10054/742
http://dspace.library.iitb.ac.in/xmlui/handle/10054/742
 
Language en