54 citations · 223 across the 23 of their papers we have counts for
15 papers · 1 filter
Computing the nearest scattering passive system
Karim Cherifi, Nicolas Gillis, Punit Sharma
In this paper, we consider linear time-invariant control systems which are bounded real, also known as scattering passive. Our main theoretical contribution is to show the equivale…
Characterizing matrices with eigenvalues in an LMI region: A dissipative-Hamiltonian approach
Neelam Choudhary, Nicolas Gillis, Punit Sharma
In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a general…
Structured eigenvalue backward errors for rational matrix polynomials with symmetry structures
Anshul Prajapati, Punit Sharma
We derive computable formulas for the structured backward errors of a complex number when considered as an approximate eigenvalue of rational matrix polynomials that carry a sy…
Doubly structured mapping problems of the form and
Mohit Kumar Baghel, Punit Sharma
For a given class of structured matrices , we find necessary and sufficient conditions on vectors $x,w\in \C^{n+m}$ and $y,z \in \C^{n}$ for which there exists $Δ=[Δ_1~Δ…
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…
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…
On the non-symmetric semidefinite Procrustes problem
Mohit Kumar Baghel, Nicolas Gillis, Punit Sharma
In this paper, we consider the non-symmetric positive semidefinite Procrustes (NSPSDP) problem: Given two matrices , find the matrix $A \in \mathbb{R}^{n,…
Characterization of the dissipative mappings and their application to perturbations of dissipative-Hamiltonian systems
Mohit Kumar Baghel, Nicolas Gillis, Punit Sharma
In this paper, we find necessary and sufficient conditions to identify pairs of matrices and for which there exists such that is positive sem…
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…
On approximating the nearest Ω-stable matrix
Neelam Choudhary, Nicolas Gillis, Punit Sharma
In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region Ω, within the complex plane. More precisely, we c…
A note on approximating the nearest stable discrete-time descriptor system with fixed rank
Nicolas Gillis, Michael Karow, Punit Sharma
Consider a discrete-time linear time-invariant descriptor system for . In this paper, we tackle for the first time the problem of stabilizing s…
Approximating the nearest stable discrete-time system
Nicolas Gillis, Michael Karow, Punit Sharma
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterizati…
Finding the nearest positive-real system
Nicolas Gillis, Punit Sharma
The notion of positive realness for linear time-invariant (LTI) dynamical systems, equivalent to passivity, is one of the oldest in system and control theory. In this paper, we con…
A semi-analytical approach for the positive semidefinite Procrustes problem
Nicolas Gillis, Punit Sharma
The positive semidefinite Procrustes (PSDP) problem is the following: given rectangular matrices and , find the symmetric positive semidefinite matrix that minimizes the…
On computing the distance to stability for matrices using linear dissipative Hamiltonian systems
Nicolas Gillis, Punit Sharma
In this paper, we consider the problem of computing the nearest stable matrix to an unstable one. We propose new algorithms to solve this problem based on a reformulation using lin…