Selected Publications:                 

 Control Theory:

1. Algebraic geometric aspects of feedback stabilization, with V. Sule,  SIAM Journal on Control and Optimization, 30:11–30, 1992.

2. An obstruction to the simultaneous stabilization of two n-D plants,  Acta Applicandae Mathematicae, 36:289–301, 1994.

3. A behavioural approach to control of distributed systems, with H. Pillai,  SIAM  Journal on Control and Optimization, 37:388–408, 1998.

4. The lattice structure of behaviours,  SIAM Journal on Control and Optimization,  39:1817–1832, 2001.                                                                                                                                                                        (Addendum to ‘The lattice structure of behaviours’, preprint.)

5. Periodic behaviours, with D. Napp and M. van der Put,  SIAM Journal on Control and Optimization, 48:4652–4663, 2010.

6. The Hautus test and genericity results for controllable and uncontrollable behaviors,  SIAM Journal on Control and Optimization, 52:32–51, 2014.

7. The generic degree of autonomy, with P. Rocha,  SIAM Journal on Applied Algebra and Geometry, 2:410–427, 2018;                                                                                                                                      Corrigendum,  3:172-174, 2019.     

8. The coarsest lattice that determines a discrete multidimensional system, with D.Pal, Mathematics of Control, Signals and Systems,  34:405 - 433, 2022.                                                              

Robotics:

1. Singularities in mechanisms II - trajectory tracking in the 3-axis wrist, Mechanisms and Machine Theory, 34:513-526, 1998.

Algebraic Theory of PDE:

1. The Nullstellensatz for systems of PDE, Advances in Applied Mathematics, 23:360-374, 1999.

2. On the dual of a flat module in TOP, Linear Algebra and its Applications, 433:1077-1081, 2010.

3. Symmetric solutions to symmetric partial difference equations,  https://arxiv.org/pdf/2310.00903.pdf, 2023.

Singular Differential Equations:

1. Filippov solutions to singular differential equations, SIAM Journal on Mathematical Analysis, 18:1463-1466, 1987.

2. Singularly perturbed systems, with P. Rabier, Applicable Analysis, 24:53-99, 1987.

Selected Talks and Lectures:

1. Controllability for systems of partial differential equations, semi-plenary talk at the MTNS, Leuven, 2004.

  2. Behaviors in the Sobolev spaces, Jan C.Willems' 70th birthday conference, Bruges, 2009.

  3. The behavioral approach to control of distributed systems, Ph.D. programme, University of Padova, 2012.                                                                                                                                                                                           https://www.dei.unipd.it/en/system/files/Catalogue2012_13_12_2011.pdf

  4. Structurally stable properties of control systems, International Conference dedicated to the 110th anniversary of L.S.Pontryagin, Steklov Institute,   Moscow, 2018.

  5. Controllability and vector potential: six lectures at Steklov, Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, 2019.                            http://www.mathnet.ru/php/conference.phtml?confid=1805

  6. Some questions in algebra that arise in the control of systems described by PDE, Workshop on Differential Algebra, Max Planck Institute, Leipzig,  2022.

__

Social Justice:

1. Two Lessons from Ashoka and Ambedkar, Round Table India, 2012.

        https://www.roundtableindia.co.in/two-lessons-from-ashoka-and-ambedkar/

2.  Manual Scavenging in India: The Banality of an Everyday Crime, with Kanthi Swaroop, Caste / A Global Journal on Social Exclusion, 2(1):67-76, 2021.

        https://journals.library.brandeis.edu/index.php/caste/article/view/299/60

sshankar.at.cmi@gmail.com

volume

 34, 

pages

405–433 (2022)                                          

Robotics:

1. Singularities in mechanisms II - trajectory tracking in the 3-axis wrist,  Mechanisms and Machine Theory, 34:513–526, 1998.

Algebraic Theory of PDE:

1. The Nullstellensatz for systems of PDE,  Advances in Applied Mathematics, 23:360–374, 1999.

2. Geometric completeness of distribution spaces,  Acta Applicandae Mathematicae, 77(2):163–180, 2003.

3. On the dual of a flat module in TOP,  Linear Algebra and its Applications, 433:1077–1081, 2010.

Singular Differential Equations:

1. Filippov solutions to singular differential equations,  SIAM Journal on Mathematical Analysis, 18:1463–1466, 1987.

2. Singularly perturbed systems (with P. Rabier),  Applicable Analysis, 24:53–99, 1987.

Expository:

1. Control theory and algebraic geometry,  Proceedings of the 21st Conference of the Ramanujan Mathematical Society, 2006.                                                                                                                                      (available at: http://modelreduction.com/contrib/Shiva.Shankar/ControlTheoryAlgebraicGeometry.pdf)