Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks Export

@article{HuiHaddad_TAC08, abstract = {<para> 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. </para>}, author = {Hui, Q. and Haddad, W. M. and Bhat, S. P.}, booktitle = {Automatic Control, IEEE Transactions on}, citeulike-article-id = {3444619}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/TAC.2008.929392}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4631513}, doi = {10.1109/TAC.2008.929392}, journal = {Automatic Control, IEEE Transactions on}, keywords = {consensus, dynamical\_systems, nonlinear\_dynamic\_systems, semistability}, number = {8}, pages = {1887--1900}, posted-at = {2008-10-24 00:07:16}, priority = {2}, title = {Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks}, url = {http://dx.doi.org/10.1109/TAC.2008.929392}, volume = {53}, year = {2008} }

TY - JOUR ID - HuiHaddad_TAC08 L3 - citeulike-article-id:3444619 N2 - <para> 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. </para> IS - 8 JF - Automatic Control, IEEE Transactions on EP - 1900 TI - Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks VL - 53 T2 - Automatic Control, IEEE Transactions on SP - 1887 KW - consensus KW - dynamical_systems KW - nonlinear_dynamic_systems KW - semistability AU - Hui, Q AU - Haddad, WM AU - Bhat, SP PY - 2008/// UR - http://dx.doi.org/10.1109/TAC.2008.929392 ER -