Artículo
Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability
Fecha de publicación:
18/02/2013
Editorial:
Institute of Electrical and Electronics Engineers
Revista:
IEEE Transactions on Automatic Control
ISSN:
0018-9286
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We address the stabilization of switching linear systems (SLSs) with control inputs under arbitrary switching. A sufficient condition for the stability of autonomous (without control inputs) SLSs is that the individual subsystems are stable and the Lie algebra generated by their evolution matrices is solvable. This sufficient condition for stability is known to be extremely restrictive and therefore of very limited applicability. Our main contribution is to show that, in contrast to the autonomous case, when control inputs are present the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices satisfy the aforementioned Lie-algebraic stability condition can become a generic property, hence substantially improving the applicability of such Lie-algebraic techniques in some cases. Since the validity of this Lie-algebraic stability condition implies the existence of a common quadratic Lyapunov function (CQLF) for the SLS, our results yield an analytic sufficient condition for the generic existence of a control CQLF for the SLS.
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Articulos(CCT - ROSARIO)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - ROSARIO
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - ROSARIO
Articulos(CIFASIS)
Articulos de CENTRO INT.FRANCO ARG.D/CS D/L/INF.Y SISTEM.
Articulos de CENTRO INT.FRANCO ARG.D/CS D/L/INF.Y SISTEM.
Citación
Haimovich, Hernan; Braslavsky, Julio H.; Sufficient conditions for generic feedback stabilizability of switching systems via lie-algebraic solvability; Institute of Electrical and Electronics Engineers; IEEE Transactions on Automatic Control; 58; 3; 18-2-2013; 814-820
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