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- Title
On approximating the nearest Ω‐stable matrix.
- Authors
Choudhary, Neelam; Gillis, Nicolas; Sharma, Punit
- Abstract
Summary: In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region Ω of the complex plane. More precisely, we consider three types of regions and their intersections: conic sectors, vertical strips, and disks. We refer to this problem as the nearest Ω‐stable matrix problem. This includes as special cases the stable matrices for continuous and discrete time linear time‐invariant systems. In order to achieve this goal, we parameterize this problem using dissipative Hamiltonian matrices and linear matrix inequalities. This leads to a reformulation of the problem with a convex feasible set. By applying a block coordinate descent method on this reformulation, we are able to compute solutions to the approximation problem, which is illustrated on some examples.
- Subjects
LINEAR matrix inequalities; CONVEX sets; MATRICES (Mathematics); LINEAR systems
- Publication
Numerical Linear Algebra with Applications, 2020, Vol 27, Issue 3, p1
- ISSN
1070-5325
- Publication type
Article
- DOI
10.1002/nla.2282