Punit Sharma

Research Area

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

Research Interests

Distance problems for matrix pencils and polynomials

Perturbation theory for linear and nonlinear eigenvalue problems

Stability of control systems

Nearness problems in control theory

Research Collaborators

Prof. Shreemayee Bora (IIT Guwahati, India), Prof. Volker Mehrmann (TU Berlin, Germany), Prof. Christian Mehl (TU Berlin, Germany), Prof. Michael Karow (TU Berlin, Germany), Prof. Nicolas Gillis (University of Mons, Belgium).

Research Visits

Research visit sponsored by IIT Delhi and University of Bari Aldo Moro, Italy to University of Bari Aldo Moro, Italy during 20-24 June, 2022.

Research visit sponsored by IIT Delhi, India and University of Mons, Belgium, to University of Mons, Belgium during May 30 - June 11, 2022 and June 25-30, 2022.

Research visit sponsored by IIT Delhi, India and University of Mons, Belgium, to University of Mons, Belgium during 01-14 July, 2019.

Research visit sponsored by IIT Delhi, India and University of Mons, Belgium, to University of Mons, Belgium during 03-14 December, 2018.

Research visit sponsored by TU Berlin, Germany, and University of Mons, Belgium, to TU Berlin, Germany during 10-23 December, 2017.

Research visit sponsored by University of Mons, Belgium, and IIT Bombay, Mumbai, to IIT Bombay during July 23 to August 5, 2017.

Research visit sponsored by TU Berlin, Germany, and University of Mons, Belgium, to TU Berlin, Germany during 11-18 March, 2017.

Research visit sponsored by TU Berlin, Germany, and University of Mons, Belgium, to TU Berlin, Germany during February 27 to March 4, 2017.

Research visit under project funded by DST, India, and DAAD, Germany, to TU Berlin, Germany during June 1-30, 2013.

Research visit under project funded by DST, India, and DAAD, Germany, to TU Berlin, Germany during December 1-30, 2011.

Seminars

"Research Seminar", Department of Mathematics, IIT Guwahati, Assam, India, December 28, 2018.
Title: Nearest stable matrix: from bad problem to good problem.

"Absolventen-Seminar Numerische Mathematik", Institute for Mathematics, TU Berlin, Germany, December 14, 2017.
Title: Port-Hamiltonian systems and various distances for control systems.

"Research Seminar", Department of Mathematics, IIT Delhi, Delhi, India, August 17, 2017.
Title: Eigenvalue backward errors of structured polynomial eigenvalue problems.

"Constrained Low-Rank Matrix Approximations", Department of Mathematics and Operational Research, University of Mons, Mons, Belgium, July 19, 2017.
Title: DH matrices and various distances to instability and stability.

"Constrained Low-Rank Matrix Approximations", Department of Mathematics and Operational Research, University of Mons, Mons, Belgium, November 10, 2016.
Title: An introduction to eigenvalue backward errors of structured polynomial eigenvalue problems.

"Absolventen-Seminar Numerische Mathematik", Institute for Mathematics, TU Berlin, Germany, June 16, 2016.
Title: Structure preserving perturbations to port-Hamiltonian systems.

"Absolventen-Seminar Numerische Mathematik", Institute for Mathematics, TU Berlin, Germany, January 16, 2016.
Title: On structured distances to instability for port-Hamiltonian systems.

Google Scholar

JOURNAL PAPER

Structured eigenvalue backward errors for rational matrix polynomials with symmetry structures,

BIT Numerical Mathematics, DOI:10.1007/s10543-024-01010-3, 2024.
(with A. Prajapati)

Characterizing matrices with eigenvalues in an LMI region: a dissipative-Hamiltonian approach,

Linear and Multilinear Algebra, DOI: 10.1080/03081087.2024.2304144, 2024.
(with N. Choudhary and N. Gillis)

On the non-symmetric semidefinite Procrustes problem,

Linear Algebra and Applications, 648, pp. 133-159, 2022.
(with M. Baghel and N. Gillis).

Optimizing the Rayleigh quotient with symmetric constraints and its application to perturbations of structured polynomial eigenvalue problems,

Linear Algebra and Applications, 645, pp. 256-277, 2022. (with A. Prajapati).

Estimation to structured distances to singularity for matrix pencils with symmetry structures: A linear algebra based approach,

SIAM Journal on Matrix Analysis and Applications, 43 (2), 740-763, 2022.
(with A. Prajapati).

Characterization of the dissipative mappings and their application to perturbations of dissipative-Hamiltonian systems,

Numerical Linear Algebra with Applications, 28 (6), 2021.
(with M. Baghel and N. Gillis).

Minimal-norm static feedbacks using dissipative Hamiltonian matrices,

Linear Algebra and Applications, pp. 0024-3795, 2020. (DOI): 10.1016/j.laa.2020.02.008
(with N. Gillis).

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

Numerical Linear Algebra with Applications, 27:e2282, 2020. https://doi.org/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

Associate Professor (since December 2024): Department of Mathematics, Indian Institute of Technology Delhi, India.

Past Affiliations

Assistant Professor (April 2018 - November 2024): Department of Mathematics, Indian Institute of Technology Delhi, India.

Postdoctoral Fellow (01.09.2016-31.03.2018): Department of Mathematics and Operational Research, University of Mons, Belgium with Prof. Nicolas Gillis .

Postdoctoral Fellow (01.09.2015-31.08.2016): Institute for Mathematics, TU Berlin, Germany, with Prof. Volker Mehrmann .

Education

Ph.D.: Ph.D. degree in Mathematics from IIT Guwahati, Guwahati, India.
Thesis Title: Eigenvalue backward errors of polynomial eigenvalue problems under structure preserving perturbations.
Thesis Supervisor: Prof. Shreemayee Bora .

M. Sc. (2010): Masters Degree in Mathematics and Computing, Indian Institute of Technology Guwahati, India.

B. Sc. (2008): Graduated in Physics, Chemistry, Maths, University Maharaja's College, Jaipur, India.

XII STD (2005): Rajasthan Public Sr. Sec. School, K. Renwal, India.

X STD (2003): Sarvottam Public Sr. Sec. School, K. Renwal, India.

Teaching at IIT Delhi

MTL101: Linear Algebra & Differential Equations (2019, 2020, 2021, 2024 (Jan.-April))

MTL104: Linear Algebra & Applications (2018, 2019, 2020 (Jul.-Dec.), 2022 (Jan.-April))

MTL100: Calculus (2022 (Sep.-Feb.))

MTL502: Linear Algebra (2021 (July-Dec.))

MTL745: Advanced Matrix Theory (2022, 2023 (Jan.-April))


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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

Teaching Excellence Award by the Director IIT Delhi, September 2021.

NBHM Travel Grant for attending ICIAM-2019 conference held at Valencia, Spain.

Awarded INSPIRE Faculty Award by Department of Science and Technology, Government of India, 7th February, 2018.

Selected for SERB-NPDF (National Postdoctoral Fellowship) by Science and Engineering Research Board, Department of Science and Technology, Government of India, 26th July, 2016.

Offered a postdoctoral scholarship in the European Research Council (ERC) project COLORAMAP by University of Mons, Belgium, 19th April, 2016.

Selected for NBHM (National Board of Higher Mathematics) postdoctoral fellowship by Department of Atomic Energy, Government of India, 10th February, 2016.

21.7.2012 - 21.7.2015 : Senior Research Fellowship, Department of Mathematics, IIT Guwahati.

21.7.2010 - 20.7.2012 : Junior Research Fellowship, Department of Mathematics, IIT Guwahati.

Secured UGC-JRF in NET Exam June 2010.

Secured All India Rank of 28 in GATE Exam 2010.

Merit Cum Scholarship in M.Sc., IIT Guwahati, 2009.

Merit Cum Scholarship in M.Sc., IIT Guwahati, 2008.

Projects

Core Research Grant by SERB India (2023-2026)
PI: Dr. Punit Sharma
Co-PI: Dr. Deepak Patil and Dr. Subashish Datta, Electrical Engineering, IIT Delhi

Mathematical Research Impact Centric Support (MATRICS) by SERB India (2022-2025)

Faculty Interdisciplinary Research Project (FIRP) Project by IIT Delhi (2019-2021)
PI: Dr. Punit Sharma
Co-PI: Dr. Deepak Patil and Dr. Subashish Datta, Electrical Engineering, IIT Delhi

New Faculty SEED grant by IIT Delhi (2018-2020)

DST Inspire Faculty Award (2018-2022)

PhD Students

Anshul Prajapati (July 2019- continuing)

Mohit Baghel (July 2018- 2023)

Thesis Title: Structured Mappings and Procrustes Problems with their Applications in Control Systems

Invited Talks

In the Department of Mathematics, University of Bari Aldo Moro, Italy, June 23, 2022.
Title: Nearness problems for matrices.

In the workshop "Matrix Computations and its application in systems, signal and control problems") organized by IIT Indore, February 16-21, 2021.
Title: Distance problems for matrix polynomials.

In the seminar series on “Linear Algebra and Operator Theory (Oselot)”, Organized by Christian Mehl (TU Berlin), Andre Ran (Amsterdam University, Netherlands) and (Jagiellonian University, Poland), November 26, 2020.
Title: Nearness problems for LTI systems using port-Hamiltonian systems.

(Delivered seven hours lecture on “Linear Algebra and its Applications”) in TEQIP , Department of Mathematics, IIT Delhi, Dec 20-24, 2020.

In the minisymposium "Eigenvalue problems: perturbation and structure preservation" at the ICIAM-2019 conference, Valencia, Spain, July 15-19, 2019.
Title: Nearness problems for LTI systems using port-Hamiltonian systems.

Department of Mathematics and Operational Research, University of Mons, Belgium, December 07, 2018.
Title: Approximating the nearest continuous-time LTI systems.

In the conference "International Conference on Mathematical Modeling and Scientific Computing" Indian Institute of Technology Indore, Madhya Pradesh, India, July 19-21, 2018.
Title: Computing nearest stable matrices.

Department of Electrical Engineering, IIT, Mumbai, India, August 04, 2017.
Title: Port-Hamiltonian systems and various distances to instability and stability.

In the minisymposium "Structured pseudospectra and stability radii" at the 88th Annual Meeting of GAMM, TU Ilmenau, Weimar, Germany March 5-10, 2017.
Title: Real structured distance to instability for linear Hamiltonian systems with perturbed dissipation.

In the minisymposium "Perturbation theory and distance problems associated with eigenvalues" at the 20th Conference of the International Linear Algebra Society (ILAS), KU Leuven, Belgium, July 11-15, 2016.
Title: Structured distances to instability for linear Hamiltonian systems with dissipation.

Conferences

The Householder Symposium XXI, on Numerical Linear Algebra at Hotel Sierra Silvana, Selva di Fasano (Br), Italy, 12-17 June, 2022.
(Paper Presented)

ORBEL32, 32nd annual conference of the Belgian Operational Research Society, Lieage, Belgium 1-2 February, 2018.
Title: On computing the distance to stability for matrices.
(Paper Presented)

Foundations of Computational Mathematics, University of Barcelona, Barcelona, Spain, 10-19 July, 2017.
Title: A new formulation for the nearest stable matrix problem.
(Paper Presented)

Householder Symposium XX on Numerical Linear Algebra, at the Inn at Virginia Tech in Blacksburg, Virginia, USA, 18-23 June, 2017.
Title: Computing nearest stable matrix pair.
(Paper Presented)

DHC, Data Sciences, University Catholique de Louvain, Louvain-La-Neuve, Belgium, 18 May, 2017.

Conference on Energy Based Modeling, Simulation, and Control of Complex Physical Systems}, TU Berlin, Germany, April 7-8, 2016.
Title: On structured distances to instability for port-Hamiltonian systems.
(Paper Presented)

ISTAM Annual Conference, Malaviya National Institute of Technology, Jaipur, India, December 16-19, 2015.
Title: On real eigenvalue backward errors of real matrix pencils and polynomials with various structures.
(Paper Presented)

DAE-day workshop, Institute for Mathematics, TU Berlin, Berlin, Germany, December 1, 2015.
Title: Structure preserving perturbations to port-Hamiltonian systems.
(Paper Presented)

International Conference on Numerical Analysis, Matrix Theory, Differential Algebraic Equations, and Control Theory, Institute for Mathematics, TU Berlin, Berlin, Germany, May 6-9, 2015.
Title : Structured eigenvalue backward errors of matrix polynomials.
(Paper Presented)

International Conference on Frontiers in Mathematics, Gauhati University, Guwahati, India, March 26-28, 2015.
Title: Structured eigenvalue backward errors of palindromic pencils.
(Paper Presented)

International Conference on Numerical Linear Algebra and its Applications (NLAA-2013), IIT Guwahati from 15-18 January, 2013.
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