2 research outputs found
Is stabilization of switched positive linear systems equivalent to the existence of an Hurwitz convex combination of the system matrices?
reserved3In this paper exponential stabilizability
of continuous-time positive switched systems is investigated. It is proved that, when dealing with twodimensional systems, exponential stabilizability can
be achieved if and only if there exists an Hurwitz
convex combination of the (Metzler) system matrices.
However, for systems of higher dimension this is not
true.
In general, exponential stabilizability corresponds
to the existence of a (positively homogeneous, concave
and co{positive) control Lyapunov function, but this
function is not necessarily smooth. The existence of
an Hurwitz convex combination is equivalent to the
stronger condition that the system is not only exponentially stable, but it also admits a smooth control
Lyapunov function. These two conditions, in turn, are
equivalent to the fact that the stabilizing switching
law can always be based on a linear co{positive control
Lyapunov function. Finally, the characterization of
exponential stabilizability is exploited to provide a
description of all the switched equilibrium points"
of a positive ane switched systemmixedF. Blanchini; P. Colaneri; M.E. ValcherF., Blanchini; Colaneri, Patrizio; M. E., Valche
Is stabilization of switched positive linear systems equivalent to the existence of an Hurwitz convex combination of the system matrices?
Abstract|In this paper exponential stabilizability
of continuous-time positive switched systems is in-
vestigated. It is proved that, when dealing with two-
dimensional systems, exponential stabilizability can
be achieved if and only if there exists an Hurwitz
convex combination of the (Metzler) system matrices.
However, for systems of higher dimension this is not
true.
In general, exponential stabilizability corresponds
to the existence of a (positively homogeneous, concave
and co{positive) control Lyapunov function, but this
function is not necessarily smooth. The existence of
an Hurwitz convex combination is equivalent to the
stronger condition that the system is not only expo-
nentially stable, but it also admits a smooth control
Lyapunov function. These two conditions, in turn, are
equivalent to the fact that the stabilizing switching
law can always be based on a linear co{positive control
Lyapunov function. Finally, the characterization of
exponential stabilizability is exploited to provide a
description of all the \switched equilibrium points"
of a positive ane switched system