Prof. Punit Sharma | Faculty Profile | IIT Delhi Abu Dhabi
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Research Areas

Numerical Linear Algebra and their Applications in Control Theory Nearness Problem for Matrix Polynomials Perturbation Theory for Linear and Nonlinear Eigenvalue Problems Stability of Control Systems Matrix Procrustes Problems

Biosketch

Punit Sharma serves as an Associate Professor in the Department of Mathematics at the Indian Institute of Technology Delhi (IIT Delhi). He obtained his Doctor of Philosophy (Ph.D.) in Mathematics from the Indian Institute of Technology Guwahati, India, under the guidance of Prof. Shreemayee Bora. He has been honoured with several awards, including the INSPIRE Faculty Award and NBHM grants, and has had postdoctoral positions at the University of Mons in Belgium and TU Berlin in Germany. As a passionate badminton player, he has competed in several competitions at various skill levels.

His research lies in Linear and Numerical Linear Algebra, with a focus on Distance problems related to matrix pencils and polynomials, Perturbation theory for linear and nonlinear eigenvalue problems, Stability of control systems, Nearness problems in control theory, and Matrix Procrustes Problems. Prof. Sharma has authored over 20 original works in leading journals focused on linear and nonlinear algebra. He has delivered multiple invited lectures at international workshops and conferences. He collaborated with many researchers, both in India and abroad.

Prof. Sharma and Prof. Nicolas Gillis have formulated a novel parameterization for the set of continuous-time stable control systems. This parametrization results in the reformulation of the difficult stability radius optimization problem into a relatively simple problem. This idea has now been generalized by several researchers to solve other distance problems occurring in engineering applications. 

Professional Highlights

Visiting Faculty, IIT Delhi - Abu Dhabi, UAE (July 2025 - present)

Associate Professor, Dept of Mathematics, IIT Delhi, India (2023 - present)

Assistant Professor, Dept of Mathematics, IIT Delhi, India (2018 - 2023)

Postdoctoral Researcher, University of Mons, Belgium (2016 - 2018)

Postdoctoral Researcher, Institute for Mathematics, TU Berpn (2015-2016)

Awards & Honours
  • 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, February, 2018.
Recent Publications
  • V. Shekhar, P. Sharma, Additional results on convergence and semiconvergence of three-step alternating iteration scheme for singular linear systems, FILOMAT, 39:15, 2025.
  • D. Lu, A. Prajapati, P. Sharma, S. Bora Eigenvalue backward errors of Rosenbrock systems and optimization of sums of Rayleigh quotient, SIAM Journal on Matrix Analysis and Applications, 46:2, 2025.
  • A. Prajapati, P. Sharma, Structured eigenvalue backward errors for rational matrix polynomials with symmetry structures, BIT Numerical Mathematics, 64:10, 2024.
  • N. Choudhary, N. Gillis, P. Sharma, Characterizing matrices with eigenvalues in an LMI region: A dissipative-Hamiltonian approach, Linear and Multilinear Algebra, 72:17, pp. 2984-2999, 2024.
  • M. Baghel, N. Gillis, P. Sharma, On the non-symmetric semidefinite Procrustes problem, Linear Algebra and Applications, 648, pp. 133-159, 2022.
  • A. Prajapati, P. Sharma, 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.
  • A. Prajapati, P. Sharma, 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, pp. 740-763, 2022.