Krishnan Balachandran

Controllability of nonlinear systems in Banach spaces: a survey

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integrodifferential systems in abstract spaces.

Controllability of nonlinear systems via fixed-point theorems

This article presents a survey of papers published on controllability of nonlinear systems, including nonlinear delay systems, by means of fixed-point principles.

Controllability of integrodifferential systems in Banach spaces

Sufficient conditions for controllability of integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem. An example is provided to illustrate the theory.

Controllability of nonlinear integrodifferential systems in Banach space

Sufficient conditions for controllability of nonlinear integrodifferential systems in a Banach space are established. The results are obtained using the Schauder fixed-point theorem.

On the controllability of fractional dynamical systems

Abstract This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

Relative controllability of fractional dynamical systems with distributed delays in control

This paper is concerned with the global relative controllability of fractional dynamical systems with multiple delays in control for finite dimensional spaces. Sufficient conditions for controllability results are obtained using Schauders fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. An example is provided to illustrate the theory.

Controllability of neutral functional integrodifferential systems in Banach spaces

Abstract Sufficient conditions for controllability of neutral functional integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem. An example is provided to illustrate the theory.

Local null controllability of nonlinear functional differential systems in Banach space

Sufficient conditions for the local null controllability of non-linear functional differential systems with unbounded linear operators in Banach space are established. The results are obtained using the semigroup of linear operators, fractional powers of operators, and the Schauder fixed-point theorem. Applications to parabolic differential systems are given.

On fractional impulsive equations of Sobolev type with nonlocal condition in Banach spaces

The objective of this paper is to establish the existence of solutions of nonlinear impulsive fractional integrodifferential equations of Sobolev type with nonlocal condition. The results are obtained by using fractional calculus and fixed point techniques.

Controllability of second-order semilinear neutral functional differential systems in Banach spaces

Abstract Sufficient conditions for controllability of semilinear second-order neutral functional differential systems in Banach spaces are established using the theory of strongly continuous cosine families. The results are obtained by using the Leray-Schauder alternative.