TY - GEN

T1 - On computing the complex passivity radius

AU - Overton, Michael L.

AU - Van Dooren, Paul

PY - 2005

Y1 - 2005

N2 - We characterize the complex passivity radius of a rational transfer matrix G(s) := C(sIn -A)-1 B + D and propose an approach to compute it. The method depends on computing the smallest structured indefinite perturbation to a Hermitian matrix that makes it singular. We consider both additive and multiplicative perturbations, giving details for the additive case. In both cases, the smallest indefinite perturbation can be efficiently computed by solving a unimodal optimization problem in a real parameter. The passivity radius can be computed by minimizing the smallest singularity-inducing multiplicative indefinite perturbation of a frequency-dependent matrix over the imaginary axis.

AB - We characterize the complex passivity radius of a rational transfer matrix G(s) := C(sIn -A)-1 B + D and propose an approach to compute it. The method depends on computing the smallest structured indefinite perturbation to a Hermitian matrix that makes it singular. We consider both additive and multiplicative perturbations, giving details for the additive case. In both cases, the smallest indefinite perturbation can be efficiently computed by solving a unimodal optimization problem in a real parameter. The passivity radius can be computed by minimizing the smallest singularity-inducing multiplicative indefinite perturbation of a frequency-dependent matrix over the imaginary axis.

UR - http://www.scopus.com/inward/record.url?scp=33847137429&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847137429&partnerID=8YFLogxK

U2 - 10.1109/CDC.2005.1583449

DO - 10.1109/CDC.2005.1583449

M3 - Conference contribution

AN - SCOPUS:33847137429

SN - 0780395689

SN - 9780780395688

T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

SP - 7960

EP - 7964

BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

T2 - 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Y2 - 12 December 2005 through 15 December 2005

ER -