Peer-Reviewed Journal Details
Mandatory Fields
Mason, O;Wirth, F
2014
March
Linear Algebra and Its Applications
Extremal norms for positive linear inclusions
Published
7 ()
Optional Fields
JOINT SPECTRAL-RADIUS COPOSITIVE LYAPUNOV FUNCTIONS DISCRETE INCLUSIONS SWITCHED SYSTEMS INVARIANT CONE STABILITY OPERATORS MATRICES INDICATOR COMPUTATION
444
100
113
For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to absolute norms. The semigroups under consideration may be generated by discrete-time systems, continuous-time systems or continuous-time systems with jumps. The existence of extremal norms is used to extend results on the Lipschitz continuity of the joint spectral radius beyond the known case of semigroups that are irreducible in the representation theory interpretation of the word. (C) 2013 Elsevier Inc. All rights reserved.
NEW YORK
0024-3795
10.1016/j.laa.2013.11.020
Grant Details