stability radii
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2021 ◽  
pp. 101-118
Author(s):  
Tamás Insperger ◽  
John Milton


IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Jesus D. Aviles ◽  
Jaime A. Moreno ◽  
Jorge A. Davila ◽  
Guillermo Becerra ◽  
Francisco Flores ◽  
...  




Author(s):  
Nicat Aliyev ◽  
Volker Mehrmann ◽  
Emre Mengi

Abstract A linear time-invariant dissipative Hamiltonian (DH) system $\dot x = (J-R)Q x$ẋ=(J−R)Qx, with a skew-Hermitian J, a Hermitian positive semidefinite R, and a Hermitian positive definite Q, is always Lyapunov stable and under further weak conditions even asymptotically stable. By exploiting the characterizations from Mehl et al. (SIAM J. Matrix Anal. Appl. 37(4), 1625–1654, 2016), we focus on the estimation of two stability radii for large-scale DH systems, one with respect to non-Hermitian perturbations of R in the form R + BΔCH for given matrices B, C, and another with respect to Hermitian perturbations in the form R + BΔBH,Δ = ΔH. We propose subspace frameworks for both stability radii that converge at a superlinear rate in theory. The one for the non-Hermitian stability radius benefits from the DH structure-preserving model order reduction techniques, whereas for the Hermitian stability radius we derive subspaces yielding a Hermite interpolation property between the full and projected problems. With the proposed frameworks, we are able to estimate the two stability radii accurately and efficiently for large-scale systems which include a finite-element model of an industrial disk brake.



2018 ◽  
Vol 39 (4) ◽  
pp. 1642-1669 ◽  
Author(s):  
Nicola Guglielmi ◽  
Vladimir Yu. Protasov


IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 52801-52813 ◽  
Author(s):  
Jesus David Aviles ◽  
Jaime A. Moreno


2017 ◽  
Vol 57 (3) ◽  
pp. 811-843 ◽  
Author(s):  
Christian Mehl ◽  
Volker Mehrmann ◽  
Punit Sharma


2016 ◽  
Vol 182 ◽  
pp. 356-371 ◽  
Author(s):  
Tsung-Chyan Lai ◽  
Yuri N. Sotskov ◽  
Alexandre Dolgui ◽  
Aksana Zatsiupa


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