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Finite-time semistability and consensus for nonlinear dynamical networks

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Title Finite-time semistability and consensus for nonlinear dynamical networks
 
Creator HUI, QING
HADDAD, WASSIM M
BHAT, SP
 
Subject control system synthesis
lyapunov methods
nonlinear systems
stability
 
Description This paper focuses on semistability and finite-time stability analysis and synthesis of systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we merge the theories of semistability and finite-time stability to develop a rigorous framework for finite-time semistability. In particular, finite-time semistability for a continuum of equilibria of continuous autonomous systems is established. Continuity of the settling-time function as well as Lyapunov and converse Lyapunov theorems for semistability are also developed. In addition, necessary and sufficient conditions for finite-time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite-time semistable if and only if it is semistable and has a negative degree of homogeneity. Unlike previous work on homogeneous systems, our results involve homogeneity with respect to semistable dynamics, and require us to adopt a geometric description of homogeneity. Finally, we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time.
 
Publisher IEEE
 
Date 2009-09-26T07:53:25Z
2011-11-25T15:35:40Z
2011-12-26T13:04:48Z
2011-12-27T05:50:49Z
2009-09-26T07:53:25Z
2011-11-25T15:35:40Z
2011-12-26T13:04:48Z
2011-12-27T05:50:49Z
2008
 
Type Article
 
Identifier IEEE Transactions on Automatic Control 53(8), 1887-1900
0018-9286
http://dx.doi.org/10.1109/TAC.2008.929392
http://hdl.handle.net/10054/1683
http://dspace.library.iitb.ac.in/xmlui/handle/10054/1683
 
Language en