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math.OC2022
Solving matrix nearness problems via Hamiltonian systems, matrix factorization, and optimization
Nicolas Gillis, Punit Sharma
In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some pre…
math.OC2021
Estimation to structured distances to singularity for matrix pencils with symmetry structures: A linear algebra-based approach
Anshul Prajapati, Punit Sharma
We study the structured distance to singularity for a given regular matrix pencil , where . This includes Hermitian, skew-He…
math.OC2019
Minimal-norm static feedbacks using dissipative Hamiltonian matrices
Nicolas Gillis, Punit Sharma
In this paper, we characterize the set of static-state feedbacks that stabilize a given continuous linear-time invariant system pair using dissipative Hamiltonian matrices. This ch…