# Punit Sharma

Assistant Professor

Department of Mathematics

Indian Institute of Technology

Hauz Khas, New Delhi 110016

Department of Mathematics

Indian Institute of Technology

Hauz Khas, New Delhi 110016

- Bio-Sketch
- Research
- Publications
- Invited Talks and Conferences
- Projects
- Fellowships and Awards
- Students
- Teaching
- Contact

## Research Area

Linear Algebra, Numerical Linear Algebra, and their Applications in Control Theory.

## Research Interests

## Research Collaborators

## Research Visits

## Seminars

Title: Nearest stable matrix: from bad problem to good problem.

Title: Port-Hamiltonian systems and various distances for control systems.

Title: Eigenvalue backward errors of structured polynomial eigenvalue problems.

Title: DH matrices and various distances to instability and stability.

Title: An introduction to eigenvalue backward errors of structured polynomial eigenvalue problems.

Title: Structure preserving perturbations to port-Hamiltonian systems.

Title: On structured distances to instability for port-Hamiltonian systems.

Google Scholar

## Journal Papers

### Minimal-norm static feedbacks using dissipative Hamiltonian matrices,

To appear in Linear Algebra and Applications, 2020. (DOI): 10.1016/j.laa.2020.02.008(with N. Gillis).

### On approximating the nearest $\Omega$-stable matrix,

To appear in Numerical Linear Algebra with Applications, 2019. (DOI): 10.1002/nla.2282 .(with N. Choudhary and N. Gillis).

### A note on approximating the nearest stable discrete-time descriptor systems with fixed rank,

Applied Numerical Mathematics, 148, pp. 131-139, 2019. (DOI): 10.1016/j.apnum.(with N. Gillis and M. Karow).

### Approximating the nearest stable discrete-time system,

Linear Algebra and its Applications, 573, pp.37-53, 2019.(with N. Gillis and M. Karow).

### Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control,

Electronic Journal of Linear Algebra, 34, pp. 526-560, 2018.(with C. Mehl and V. Mehrmann).

### Finding the nearest positive-real system,

SIAM Journal on Numerical Analysis,56(2), pp. 1022-1047, 2018.(with N. Gillis).

### Computing nearest stable matrix pairs,

Numerical Linear Algebra with Applications, 25(5), 2018. (DOI): 10.1002/nla.2153.(with N. Gillis and V. Mehrmann).

### A semi-analytical approach for the positive semidefinite Procrustes problem,

Linear Algebra and Applications, 540, pp. 112-137, 2018.(with N. Gillis).

### On computing the distance to stability for matrices using linear dissipative Hamiltonian systems,

Automatica, 85, pp. 113-121, 2017.(with N. Gillis).

### Stability radii for real linear Hamiltonian systems with perturbed dissipation,

BIT Numerical Mathematics 2017, 57:3, 811-843.(with C. Mehl and V. Mehrmann).

### Stability radii for linear Hamiltonian systems with dissipation under structure-preserving perturbations,

SIAM Journal on Matrix Analysis and Applications 2016 37:4, 1625-1654.(with C. Mehl and V. Mehrmann).

### Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures,

SIAM Journal on Matrix Analysis and Applications 2015 36:2, 393-416.(with S. Bora, M. Karow, and C. Mehl).

### Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures,

SIAM Journal on Matrix Analysis and Applications 2014 35:2, 453-475.(with S. Bora, M. Karow, and C. Mehl).

## Conference Paper

### Reconstruction of Aggregation Tree in spite of Faulty Nodes in Wireless Sensor Networks,

in Proc. of 6th IEEE International Conference on Wireless Communication and Sensor Networks (WCSN'10), (IEEE Press), Allahabad, India.(with P. S. Mandal)

## Present Affiliation

## Past Affiliations

## Education

Thesis Title: Eigenvalue backward errors of polynomial eigenvalue problems under structure preserving perturbations.

Thesis Supervisor: Prof. Shreemayee Bora .

## MTL101: Linear Algebra & Differential Equations (Jan-April 2019, 2020)

## MTL104: Linear Algebra & Applications (Jul-Nov 2018,2019)

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## Courses I assisted in IIT Guwahati

Mathematics -I (Real analysis and linear algebra), 2012 (July-Dec.).

Mathematics -II (Ordinary differential equations and multi-variable calculus), 2012, 2014 (Jan.-April).

Mathematics -III (Complex analysis and partial differential equations), 2014 (July-Dec.).

Matrix Computation, 2013, 2014 (July-Dec.).

Numerical Linear Algebra, 2013 (Jan.-April).

## Awards and Fellowships

## Projects

PI: Dr. Punit Sharma

Co-PI: Dr. Deepak Patil and Dr. Subashish Datta, EE, IIT Delhi

## PhD Students

## MTec Students

Title: Distance to $\alpha$-stability for matrices.

## MSc Students

Title: Indefinite Linear Algebra.

## Btec Students

Title: Eigenvalue Computations.

Title: Generalized Eigenvalue Problem.

## Invited Talks

Title: Nearness problems for LTI systems using port-Hamiltonian systems.

Title: Approximating the nearest continuous-time LTI systems.

Title: Computing nearest stable matrices.

Title: Port-Hamiltonian systems and various distances to instability and stability.

Title: Real structured distance to instability for linear Hamiltonian systems with perturbed dissipation.

Title: Structured distances to instability for linear Hamiltonian systems with dissipation.

## Conferences

Title: On computing the distance to stability for matrices.

(Paper Presented)

Title: A new formulation for the nearest stable matrix problem.

(Paper Presented)

Title: Computing nearest stable matrix pair.

(Paper Presented)

Title: On structured distances to instability for port-Hamiltonian systems.

(Paper Presented)

Title: On real eigenvalue backward errors of real matrix pencils and polynomials with various structures.

(Paper Presented)

Title: Structure preserving perturbations to port-Hamiltonian systems.

(Paper Presented)

Title : Structured eigenvalue backward errors of matrix polynomials.

(Paper Presented)

Title: Structured eigenvalue backward errors of palindromic pencils.

(Paper Presented)

Title: Structured backward error of approximate eigenvalues of T-palindromic polynomials.

(Paper Presented)

## Dr. Punit Sharma

Room 428(F) block-II,

Department of Mathematics,

Indian Institute of Technology Delhi,

Hauz Khas, New Delhi- 110016, India

Ph: +91-11-2659 1475

E-Mail: punit.sharma<AT>maths.iitd.ac.in