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Your search keyword '"George, Raju K."' showing total 123 results
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123 results on '"George, Raju K."'

1. Controllability and Observability of Heterogeneous Networked Systems with Non-uniform Node Dimensions and Distinct Inner-Coupling Matrices

Author

Thomas, Aleena, Ajayakumar, Abhijith, and George, Raju K.

Subjects
Mathematics - Optimization and Control
Abstract

In this paper we extend the work in the conference paper 'On the Controllability and Observability of Heterogeneous Networked Systems with distinct node dimensions and inner-coupling matrices' wherein the controllability and observability of a heterogeneous networked system with distinct node dimensions were studied. This paper adds to the conference paper a necessary and sufficient condition for controllability of the networked system. The result demonstrates the dependence of controllability of the network on factors like network topology, inner interactions among nodes and nodal dynamics. The result is formulated by characterizing the left eigenvectors of the network state matrix. Another necessary and sufficient condition for controllability, which is a reformulation of the \textit{Popov-Belevitch-Hautus} controllability condition, a necessary and sufficient condition for observability of the networked system and certain necessary conditions for controllability of the networked system are the other results established in this paper. Variants of these results under certain specific network topologies like path, cycle, star and wheel are also discussed., Comment: Extension of the paper presented in ICCAIRO 2023

Published
2024

2. Exact Null Controllability of Non-Autonomous Conformable Fractional Semi-Linear Systems with Nonlocal Conditions

Author

Jha, Dev Prakash and George, Raju K.

Subjects
Mathematics - Optimization and Control
Abstract

This paper investigates the existence and uniqueness of the mild solutions and the exact null controllability for a class of non-autonomous parabolic evolution systems with nonlocal conditions in Hilbert spaces. We present sufficient conditions for achieving exact null controllability in these systems using the theory of linear evolution systems and the Schauder fixed point theorem. Importantly, our results do not require the compactness or Lipschitz conditions for the function \( g \) in the nonlocal conditions, which are often needed in other studies. We also provide an example to demonstrate the practical application of our results., Comment: 20 pages, 0 figure

Published
2024

3. Existence and uniqueness of mild solutions and evolution operators for a class of non-autonomous conformable fractional semi-linear systems and their exact null controllability

Author

Jha, Dev Prakash and George, Raju K

Subjects
Mathematics - Optimization and Control, Mathematics - Analysis of PDEs
Abstract

This paper explores key aspects of the theory and applications of conformable fractional order systems. It begins by establishing the existence and uniqueness of the evolution operator for a class of non-autonomous homogeneous systems. Using the Schauder fixed point theorem and the theory of linear evolution systems, we delve into the existence of mild solutions for a class of non-autonomous conformable fractional semi-linear systems. Additionally, the paper addresses the exact null controllability of abstract systems. We present an example to demonstrate the efficiency of the results., Comment: 24 Pages, 0 figures

Published
2024

4. Solved Problems—Linear Transformations

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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5. Solved Problems—Vector Spaces

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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6. Applications

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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7. Solved Problems—Normed Spaces and Inner Product Spaces

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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8. Solved Problems—Eigenvalues and Eigenvectors

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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9. Bounded Linear Maps

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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10. Solved Problems—Preliminaries

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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11. Solved Problems—Bounded Linear Maps

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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12. Vector Spaces

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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13. Eigenvalues and Eigenvectors

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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14. Linear Transformations

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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15. Normed Spaces and Inner Product Spaces

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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16. Preliminaries

Author

George, Raju K., Ajayakumar, Abhijith, George, Raju K., Editor-in-Chief, Kesavan, S., Editor-in-Chief, Ramdorai, Sujatha, Editor-in-Chief, Shalabh, Editor-in-Chief, Paranjape, Kapil Hari, Associate Editor, Raghavan, K. N., Associate Editor, Ravichandran, V., Associate Editor, Shah, Riddhi, Associate Editor, Sinha, Kaneenika, Associate Editor, Verma, Kaushal, Associate Editor, Zuazua, Enrique, Associate Editor, and Ajayakumar, Abhijith

Published
2024
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19. Controllability of LTI Networked Systems with Heterogeneous Dynamics

Author

Ajayakumar, Abhijith and george, Raju K

Subjects
Mathematics - Optimization and Control, Mathematics - Dynamical Systems
Abstract

In this paper, a necessary and sufficient condition for the controllability of networked systems with heterogeneous dynamics is established where the nodes are higher dimensional linear time invariant systems and the network topology is directed and weighted. The controllability of networked system over some specific topologies are also examined and some non-controllability results are obtained. The theoretical results are demonstrated with examples.

Published
2020
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21. Generalized Seikkala Derivatives and their application for solving Fuzzy Wave Equation

Author

Pirzada, U. M. and George, Raju K.

Subjects
Mathematics - General Mathematics
Abstract

This paper presents the new generalized Seikkala derivatives (gS- derivatives) of fuzzy-valued functions. The solution of fuzzy wave equation is proposed and analyzed using gS-derivatives whose crisp solution is expressed in terms of Fourier series., Comment: Submitted to journal

Published
2019

36. CONTROLLABILITY OF LINEAR IMPULSIVE SYSTEMS-AN EIGENVALUE APPROACH.

Author

MUNI, VIJAYAKUMAR S. and GEORGE, RAJU K.

Subjects
CONTROLLABILITY in systems engineering, EIGENVALUES, LINEAR systems, TIME-varying systems, MATRICES (Mathematics)
Abstract

This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthe- sised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are pro- vided that demonstrate|for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems. [ABSTRACT FROM AUTHOR]

Published
2020
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50. Trajectory Controllability of Fractional Integro‐Differential Systems in Hilbert Spaces.

Author

Govindaraj, Venkatesan and George, Raju K.

Subjects
CONTROLLABILITY in systems engineering, NUMERICAL analysis, FRACTIONAL differential equations, INTEGRO-differential equations, DYNAMICAL systems, NONLINEAR systems
Abstract

Abstract: In this paper, sufficient conditions for trajectory controllability of nonlinear fractional integro‐differential systems involving Caputo fractional derivative of order α∈(1,2] in finite and as well as in infinite dimensional Hilbert spaces are obtained. Our tools of study include set‐valued functions, theory of monotone operators and α‐order cosine family of operators. The main results are well illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]

Published
2018
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