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  • 11:03 PM, Monday, 10 Aug 2020

Department of Mathematics
Raju K. George, Ph.D.
Dean(R&D), Dean(Students Welfare), Sr. Professor
Tel:+91-471- 2568413 / +91-471-2568490
Fax:+91-471-2568467 /

  • Ph.D. (IIT, Bombay)

Course Offered
  • Engineering Mathematics-Differential Equations, Calculus of Variations, Mathematical theory of Control
  • Soft Computing, Artificial Neural Networks

  • Currently Teaching Undergraduate and Post-Graduate courses at Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, India as  Professor and Head of Mathematics.
  • Professor and Head of Mathematics at the University Institute of Chemical Technology, Mumbai, August 2007 – Sept 2007.
  • Teaching Undergraduate Courses at the University of Delaware as visiting Professor during 2002-2004, (2 years).
  • 12 years as associate Professor in the M S University of Baroda Baroda, teaching Engineering Undergraduate students and post-graduate students of Applied Mathematics programme.

Research Work / Area
  • Functional Analysis
  • Mathematical Control Theory
  • Soft Computing and Machine Learning
  • Industrial Mathematics - Modelling and Simulation
  • Orbital Mechanics
  1. Ordinary Differential Equations: Principles and Applications, Cambridge University Press, UK, 2017(with A.K. Nandakumaran, P.S. Datti).
  1. Chapter 3 : Neural Networks, Lecture Notes on Scientific Computing – Theory and practices, edited by M C Joshi, G B Pant University of Agricul. And technol., Pantnagar, 2006
  2. Chapter 2 : Linear Systems and Stability Analysis, Lecture Notes of Instructional Workshop on Differential equations: Theory and computation, Department of Mathematics, Indian Institute of Science, Bangalore, pp. 37-58, 2000,
  3. Three Review Articles in the journal of Indian Institute of science, Bangalore, 1993-1997.
  1. Stochastic stability of mode-dependent Markovian jump inertial neural networks, The Journal of Analysis pp 1–18, DOI (2018) (with R. Krishnasamy).
  2. Existence and Uniqueness of Classical and Mild Solutions of Generalized Impulsive Evolution Equation, Int. J. Nonlinear Sci. Numer. Simul. 19, no. 7-8, 775–780, 2018-10-25 (2018) (with Vishant Shah, Jaita Sharma, P. Muthukumar).
  3. Controllability of fractional order semilinear systems with a delay in control, Indian J. Math. 60 (2018), no. 2, 311–335 (2018) (with Govindaraj Venkatesan).
  4. Controllability of semilinear impulsive control systems with multiple time delays in control, IMA Journal of Mathematical Control and Information, 00, 1–31, doi:10.1093/imamci/dny011 (2018) (with Vijayakumar S Muni).
  5. Numerical Approach for the Controllability of Composite Fractional Dynamical Systems, Journal of Applied Nonlinear Dynamics 7(1), 59-72, (2018) (with Venkatesan Govindaraj, Krishnan Balachandran).
  6. On the Controllability of Linear and Semilinear Impulsive Systems, Numerical Functional Analysis and Optimization, 39, no. 8, 843–864,, (2018) (with Bhaskar Dubey).
  7. Controllability of linear impulsive matrix Lyapunov differential systems with delays in the control function, Kybernetika (Prague), 54, no. 4, pp. 664–698 (2018) (with Muni Vijayakumar S).
  8. Design and analysis of weak stability boundary trajectories to Moon, Astrophys. Space Sci. 363, no. 8, Paper No. 161, 10 pp (2018) (with Dutt Pooja, Anilkumar A. K.)
  9. Trajectory controllability of fractional integro-differential systems in Hilbert spaces, Asian Journal of Control, Vol. 20, No. 5, pp.
    1994–2004, DOI: 10.1002/asjc.1685 (2018) (with V. Govindaraj).
  10. Functional approach to observability and controllability of linear fractional dynamical systems, Journal of Dynamical Systems and Geometric Theories,  15 (2017), 111-129  (with V. Govindaraj).
  11. Controllability of fractional dynamical systems: A functional analytic approach, Mathematical Control and Related Fields,  7 (2017), 537-562  (with V. Govindaraj).
  12. Controllability of iterative fractional integro-differential systems in Banach spaces, Indian Journal of Mathematics,  59 (2017), 161-187 (with V. Govindaraj).
  13. Trajectory controllability of fractional dynamical systems, Journal of Control and Decision, Vol. 4, No. 2, pp. 114-130, (2017) (with V. Govindaraj and M. Malik)
  14. Trajectory Controllability of Semilinear Parabolic System, Journal of Analysis, Springer, pp. 1-9, (2017). doi:10.1007/s41478-017-0048-3. (with Ruchi S and Sarvesh Kumar).
  15. Dynamics of Weak Stability Boundary Transfer Trajectories to Moon, Astrophysics and Space Science, Vol. 361, No. 11, pp. 361-368 (2016) (with Pooja Dutt, A K Anilkumar).
  16. Trajectory Controllability of the Nonlinear Systems Governed by Fractional Differential Equations, Differential Equations and Dynamical Systems, 1-9, 10.1007/s12591-016-0292-z (2016) (with M.  Malik).
  17. Identification of an unknown coefficient in KdV equation from final time measurement, Article in Journal of Inverse and Ill-Posed Problems 24(4), DOI: 10.1515/jiip-2016-0011(2016) (with Kumarasamy Sakthivel, Soundararajan Gnanavel, Alemdar Hasanov).
  18. Trajectory controllability of fractional dynamical systems, Journal of Control and Decision, pp.1-17, (2016), (with V. Govindaraj and M. Malik).
  19. Controllability and Impulsive Matrix Lyapunov Systems, Applied Mathematics and Computation, Vol.254, PP.327-339 (2015) (with Bhaskar Dubey). 
  20. Optimal Control of Discrete Volterra Systems - A Classical Approach, International Journal of Applied Mathematics and Computation (IJAMC) (2014) (with T. P. Shah).
  21. A note on the evolution of solutions of a system of ordinary differential equations with fuzzy initial conditions and fuzzy inputs, To appear in Journal of Uncertain Systems(2013) (with Bhaskar Dubey).
  22. Controllability of semilinear matrix Lyapunov systems, Electronic Journal of Differential Equations (42), 1-12 (2013) (with B. Dubey).
  23. On The Systems of Fuzzy Differential Equations, Advances in Fuzzy Set and Systems Vol. 13, No: 1, pp. 61-75 (2012) (with B Dubey).
  24. Estimation of controllable Initial Fuzzy States of Linear Time Invariant Dynamical Systems, Communications in Computer and Information Science, Vol.283, 316-324, (2012) (with B Dubey).
  25. Controllability of Discrete Volterra Systems, International Journal of Applied Mathematics and Computation, Volume 3(3), pp 206-215(2011) (with T. P. Shah).
  26. Controllability of Urysohn integral inclusions of Volterra type, Electron. J. Differential Equations, No. 79, 12 pp, (2010) (with Angell, Thomas S, Sharma, JaitaPankaj).
  27. Trajectory controllability of nonlinear integro-differential system, Journal of Franklin Institute, 347 (7), pp.1065-1075 (2010) (with Chalizhajar D.N, Nandakumar A.K and Acharia F.S).
  28. Asymptotic Stability of Semi-linear Discrete Dynamical Systems Involving(sp) Matrix, Nonlinear Studies, Vol. 16, No. 1, pp.23-29(2009) (with T.P. Shah).
  29. Application of Artificial Neural Networks to Predict the Probability of Extreme Rainfall and Comparison with the Probability by Fisher Tippet Type-II Distributions, International Journal of Applied Mathematics and Computations, Vol 1(3), pp.118-131 (2009) (with M.S. Kulshretha and A.M. Shekh).
  30. Accurate solution estimate and asymptotic behaviour of Nonlinear Discrete system, Sutra: International Journal of Mathematical Science Education, Vol. 1, No. 1, pp. 9-15 (2008) (with T.P. Shah).
  31. Steering control of Semilinear Discrete dynamical system, Journal of Indian Institute of Science, Vol. 87:4, pp. 485-489 (2007)(with T.P. Shah).
  32. Prediction of Annual Rainfall By Double Fourier Series and Artificial Neural Network, Int. J. of Neural, Parallel and Scientific computations, vol.15, no.4 pp.539-546 (2007)(with M.S. Kulshretha and A.M. Shekh).
  33. Prediction of the weekly Rainfall probabilities by Gamma distribution and Artificial Neural Networks: J. of Agro Meteorology, vol. 9, no. 2, pp. 196-202 (2007)(with M.S. Kulshretha and A.M. Shekh).
  34. Exact Controllability of Nonlinear Third-Order Dispersion, Journal of Mathematical Analysis and Applications, Vol. 332,pp.1028-1044(2007)(with A.K. Nandakumaran and D.N. Chalishajar).
  35. Controllability of Matrix Second Order Systems: A Trigonometric Matrix Approach, Electronic J. Diff Eqns, Vol. 2007,No. 80, pp.1-14 (2007)(with H. Jaita).
  36. Controllability and Steering control by Spectral Method, Mathematics, Computing and Modeling, Edit. P Balasubramaniam and R Uthayakumar, Allied Publishers, pp. 29-38, (2007)(with H. Jaita).
  37. Controllability of Matrix Second Order Systems- Cosine and Sine Operator Approach, Mathematics, Computing and Modelling, Edit. P Balasubramaniam and R Uthayakumar, Allied Publishers, pp. 11-20, (2007)(with H. Jaita).
  38. Exact Controllability of Nonlinear Impulsive Systems, (to appear in the Proceedings of Fifth International Conference on Dynamical Systems and Applications, 2007, Atlanta, USA)(with H. Jaita).
  39. Prediction of Hourly Air Temperature by Using Double Fourier Series, (to appear in the Proceedings of Fifth International Conference on Dynamical Systems and Applications, 2007, Atlanta, USA)(with M.S. Kulshretha and A.M. Shekh).
  40. Exact Controllability of Generalized Hammerstein Type Integral Equation with Applications, Elect. J. Differential Equations, Vol. 142, pp1-15 (2006)(with A.K. Nandakumaran and D.N. Chalishajar).
  41. Exact Controllability of Generalized Hammerstein Type Equation Industrial Mathematics, Edited by M. C. Joshi, A. K. Pani and A. V. Sabnis, Narosa Publishing House, New Delhi, pp. 61-70 (2006)(with A.K. Nandakumaran and D.N. Chalishajar).
  42. Controllability of Second order Semilinear Neutral Functionasl Differential Inclusion in Banach Space. , Meditaranean Journal of Mathematics, vol 1 , pp. 463-477,(2004)(with A.K. Nandakumaran and D.N. Chalishajar).
  43. Exact Controllability of a Semilinear Thermoelastic System Numerical Functional Analysis and Optimization, Vol 25(3&amp4),271-285, (2004)(with A.K. Nandakumaran).
  44. Prediction of the rainfall of the Anand station of Gujarat using Artificial Neural Network” Jr. of Agro Meteorology. Vol. 6, pp 233-236, (2004)(with M.S. Kulshreths and A.M. Shekh).
  45. Solvability and Controllability of Controlled Lienard System, Indian Journal of Mathematics, Vol 45, pp. 59-69, (2003)(with R.C. Shah).
  46. Prediction of soil temperature by using Artificial Neural Networks Algorithms, Nonlinear Analysis, vol. 47, pp. 1737-1748, (2001).
  47. On the Controllability of a Class of nonlinear Stochastic Systems, Systems and Control Letters , Vol. 44 , pp. 25-34, (2001)(with A. Arapostathis and M.K Ghosh).
  48. Prediction of Soil Temperatures Using Artificial Neural Networks.” Jr. of Agro Meteorology.Vol.(3) 1&2:, pp 169-173, (2001)(with S. Ramamohan, M.S. Kulshretha, A.M. Shekh and H.Jaita).
  49. MLE of Location Parameter of Cauchy Distribution, Gujarat Statistical Review , Vol. 26(1999) and Vol. 27,pp.61-68, (2000)(with A.G. Phatak).
  50. A note on Controllability of Impulsive Systems, Journal of Mathematical Analysis and Applications 241, pp.276-283(2000)(with A.K. Nandakumaran and A. Arapostathis).
  51. Controllability of Hopfield Networks, Proceedings of Brain-Machine workshop, 2000 held at Middle East Technical University, Ankara, Turkey during 20-22nd December 2000, Ed. U Halici et. al , pp. 93-102, (2000).
  52. Controllability of Singular system Using alpha times Integrated Functions, Proceedings of the 45th congress of the Indian society of Theoretical and Applied Mechanics, Editor D.K. Tripathy, pp.112-120, IIT Kharagpur, ( 2000)(with D.N. Chalishajar).
  53. Stability and Controllability of Hopfield Neural Network, Proceedings of international Conference on Mathematical Modelling of Nonlinear Systems,IIT Kharagpur, Vol.1, (1999)
  54. Observability Analysis of Hopfield Type Neural Networks, J. of the M.S. University of Baroda, Vol. 44-45,No.3, pp. 49-55,(1997-98)(with Purnima K. Pandit).
  55. Trajectory Controllability of 1-dimensional Nonlinear Systems, Proceedings of the Research Seminar in honour of Professor M N Vasavada, Department of Mathematics, S.P.University, Anand, pp. 43-48,(1996).
  56. Approximate Controllability of Non-autonomous Semilinear Systems. Nonlinear Analysis, Theory, Methods and Application, Vol.24, pp.1377-93,( 1995)
  57. Approximate Controllability of Semilinear Systems using Integral Contractors, Numerical Function Analysis and Optimization, vol.13. pp. 127-138, (1995).
  58. Partial Exact Controllability of a non-linear system. Revista Mathematica d al Universidad Coplutense de Madrid, Vol.8, No.1, pp. 181-196, (1995)(with A.K. Nandakumaran).
  59. Partial exact controllability of a Linear Thermoelastic System, Indian Journal of Mathematics, Vol.37, No.2, pp 165-174, (1995)(with A.K. Nandakumaran).
  60. Observability of a Class of Nonlinear Abstract Systems, Mathematical theory of Control, Edited by M.C.Joshi and A.V.Balakrishnan, Lectutre Notes in Pure and Applied Math. Vol. 142, Marcell-Decker Inc.,NY, pp.143- 160, (1993).
  61. On Controllability of Predator-Prey Systems, Journal of Optimization Theory and Applications, Vol.74, No.2, pp. 243-258, (1992)(with Mohan C. Joshi).
  62. Controllability of Nonlinear Systems, Numerical functional Analysis and Optimization, Vol.10(1&2), pp.139-166, (1989)(with Mohan C. Joshi). 
  1. Delivered a talk in the workshop Open source Tools for Academic Activities on “GNU Octave” organized by Rajagiri School of Engineering and Technology, on 23rd February 2013.
  2. Delivered a talk in the National Seminar on “Mathematics in Space Technology” in Little Flower College on 14th February 2013.
  3. Delivered a talk on “Nonlinear Differential Equations and Linearization Techniques” at Gandhigram Rural University, Gandhigram on 4th January 2013.
  4. Chaired a Discussion Meeting on Formation of a Forum on Control and Inverse Problems in the “ICTS Winter School on Stochastic Analysis and Control of Fluid Flow”, on 14th December 2012, IISER Trivandrum.
  5. Participated in the “Indo-European Modelling” Week at M.S University of Baroda as a resource person in the DST Sponsored NPDE (National Programme for Differential Equations – Theory, Applications and Computation) during 5th to 7th December 2012.
  6. Delivered a series of lectures on “Controllability of Linear Systems” in the workshop on Mathematical Theory of Control and Numerics (MTCN) during 21st November – 30th November 2012.
  7. Delivered a series of lectures on “Differential Equations” in the NPDE-TCA (National Programme on Differential Equations: Theory, Computation and Applications) from                  14th May – 18thMay, 2012. IMA, Bhubaneshar.
  8. Delivered a lecture on “Transition Matrix Technique for the Computation of Steering Controls in Artificial Satellite” in National Conference on Applied Mathematics (INCAM-2012) from 4th May-5th May, 2012, Parul Institute of Engineering and Technology, Baroda.
  9. Delivered a Talk on “Importance of Mathematics for +2 students in science streams for choosing their career” at Sarvodaya Central School, Nalanchira, Trivandrum, 26th March 2012.
  10. Delivered an Invited Talk on “Using MATLAB for Mathematical Problem Solving” in the Two-Day Seminar on Computation and Programming, University College, Trivandrum, 23rd -24th March 2012.
  11. Delivered a Talk on MATLAB for at Darshana Book Exhibition on behalf of National year of Mathematics, Kottayam, 1st February, 2012.
  12. Delivered series of  lectures on “C0-Semigroup operators for Control Systems ” at IISc, Bangalore on  23rd January to 27th January, 2012.
  13. Delivered a talk on “Optimal Control of Dynamical Systems” 56th congress of the Indian Society of Theoretical and Applied Mechanism (ISTAM) at NIT Surat from 19th to 21st December, 2011.
  14. Delivered a lecture in the DST sponsored INSPIRE Programme, at SVNIT, Surat on 26th August, 2011.
  15. “Application of differential equations to Control theory”, A refresher course in Mathematics, Academic Staff College, May 18, 2010.
  16. “Dynamical Systems described by Differential Equations”, 75th annual conference (Platinum Jubilee), of the Indian Mathematicians, The Kalasalingam University, Anand Nagar, Dec 27-30, 2009.
  17. “Control of Artificial Satellites”, Trivandrum, Kerala, Dec 28-29, 2009.
  18. “Finite Dimensional Controllability Theory”, Workshop on PDE and Related Analysis, Department of Mathematics, Indian Institute of Science, Bangalore, Sept 07-11, 2009.
  19. “Basics of Matlab”, Workshop on Matlab and Simulink for VSSC Scientist, IIST Thiruvananthapuram, July 07-10, 2009.
  20. Introduction to Neural Networks, Invited Talk, Department of Physics, University of Kerala, Kariyavattom, April 23, 2009.
  21. “Differential Equations and its Applications to Control Theory”, Invited Talk, Scott Christian College, Nagercoil, April 03, 2009.
  22. Delivered two invited lectures on Matlab in the AICTE sponsored Staff Development Programme on “Applications of Mathematical Sciences and Soft Computing” held at Mathematics Section of AS & H Department, SVNIT, Surat, Dec 8-12, 2008.
  23. Delivered a talk on “Solvability of System of Equations Ax=b by using Generalized Inverse”, in the annual meeting and memorial talk to commemorate the late Prof. K. N. G. Unnithan,, Sasthamcotta, Nov 6th, 2008.
  24. Delivered a talk on “Theory of Control – A functional Analytic Approach”, in the National Seminar on Functional Analysis held at the D.B.Pampa College, Parumala, Thiruvalla, Sept 25-27, 2008.
  25. Delivered three lectures on “Introduction to maple and solutions of Differential equations by using Maple” at the department of mathematics, Dr BAM University, Aurangabad, Mar 13-15, 2008.
  26. Delivered an invited talk on “Diffrential Equations and its Applications to Controls” in the Department of mathematics, University of Calicut, Jan 8, 2008.
  27. Chaired a session and gave a talk on ‘Controllability of Matrix Second Order Systems – A Trigonometric Matrix Approach’ in the Fifth International Conference on Dynamic Systems and Applications, May 30 – June 2, 2007 held at Morehouse College Atlanta, Georgia, USA.
  28. Delivered a talk on “Controllability of nonlinear diffusion system using zonal controls” in the Indo-French video conference at IISc, Bangalore, Oct 25-26, 2007.
  29. Visited the Morehouse College, Atlanta, USA, in May 2003 and gave a talk on ‘Controllability of Nonlinear Thermoelastic systems’ in the Fourth International conference on Dynamic Systems and Applications.
  30. Visited the University of Texas at Austin, Austin, USA, and had research discussion meeting in June, 2002.
  31. Visited the University of Delaware, Delaware, USA, in June 2002 and gave a talk on ‘Nonlinear controllability Problems’.
  32. Visited the State University of New York at Buffalo, USA, in June , 2002 and gave a talk on ‘the Dynamics of Nonlinear Control Systems’.
  33. Visited The University of Manitoba at Winnipeg, Canada, in June, 2002 and gave a talk on ‘controllability of Nonlinear systems’ in the department of Mathematics.
  34. Visited the University of North Carolina at Wilmington, USA, in May 2002 and gave a talk on ‘Controllability of Nonlinearly Perturbed systems’ in the International conference on Dynamical Systems and Differential Equations held at the same place.
  35. Visited the Middle East Technical University, Ankara, Turkey in December, 2000. Gave a talk on ‘Controllability of Hopfield Networks’ in Brain-Machine workshop 2000 held at the same place.
  36. Visited University of Catania and University of Milan, Italy in July 2000. Gave a talk on ‘Prediction of Soil Temperature by using Artificial neural Networks’ in World Congress of Nonlinear Analysts 2000 at Catania, Italy.



 1. B.Tech          Applied  Mathematics   Calculus of Variations

 2. M.Tech         Artificial Neural Networks

 3. PhD  Level Courses :   Mathematical Theory  of Control

Assignment : MA221 – Calculus of Variations (IV Semester)

Date of Submission : 25th March 2014

Lecture Notes – 1 :  Calculus of Variations

This Odd Semester (July-Octber, 2015), I am teaching  the MTech Course

" Mathematics for Control Theory"

The course involves:

1. Advanced Linear Algebra

2. Normed Linear Spaces

4. Operators on Normed Linear Spaces

5. Hilbert Spaces

6. Controllability and Observability - Operator Theoretic Approach

7. Generalized Inverses abd computation of steerring controls for linear systems.


1. R W Brocket : Linear Control Systems

2. S D Sontag: Mathematical Theory of Control