54 citations · 223 across the 23 of their papers we have counts for
25 papers
Nearest structured matrix having an eigenvalue with prescribed lower bounds of algebraic and geometric multiplicities
H. Lalhriatpuia, Tanay Saha, Punit Sharma
We study the problem of perturbing a given matrix X belonging to a subspace S of linearly structured real matrices of order n to its nearest counterpart Y=X+D, where D belongs to S…
Computing the nearest -admissible descriptor dissipative Hamiltonian system
Vaishali Aggarwal, Nicolas Gillis, Punit Sharma
For a given set , a matrix pair is called -admissible if it is regular, impulse-free and its eigenvalues lie inside the region . In this paper,…
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…
Additional results on convergence and semiconvergence of three-step alternating iteration scheme for singular linear systems
Vaibhav Shekhar, Punit Sharma
The three-step alternating iteration scheme for finding an iterative solution of a singular (non-singular) linear systems in a faster way was introduced by Nandi {\it et al.} [Nume…
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…
Carroll covariant scalar fields in two dimensions
Arjun Bagchi, Aritra Banerjee, Sudipta Dutta +2
Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons and tensionless strin…
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…
Optimizing Rayleigh quotient with symmetric constraints and their applications to perturbations of the structured polynomial eigenvalue problem
Anshul Prajapati, Punit Sharma
For a Hermitian matrix and symmetric matrices , we consider the problem of computing the supremum of $\left\{ \frac…
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…
Tensionless Tales: Vacua and Critical Dimensions
Arjun Bagchi, Mangesh Mandlik, Punit Sharma
Recently, a careful canonical quantisation of the theory of closed bosonic tensionless strings has resulted in the discovery of three separate vacua and hence three different quant…
BMS Field Theories and Weyl Anomaly
Arjun Bagchi, Sudipta Dutta, Kedar S. Kolekar +1
Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are natural…
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…
Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge
Sayid Mondal, Boudhayan Paul, Gautam Sengupta +1
We utilize a holographic construction to compute the entanglement negativity for bipartite mixed state configurations of a single subsystem in s with a conserved charge dual…
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…
Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control
Christian Mehl, Volker Mehrmann, Punit Sharma
Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained und…
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…
Computing nearest stable matrix pairs
Nicolas Gillis, Volker Mehrmann, Punit Sharma
In this paper, we study the nearest stable matrix pair problem: given a square matrix pair , minimize the Frobenius norm of such that is a stable…
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…