Journal ArticleDOI
Local null controllability of nonlinear functional differential systems in Banach space
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In this paper, sufficient conditions for the local null controllability of non-linear functional differential systems with unbounded linear operators in Banach space are established using the semigroup of linear operators, fractional powers of operators, and the Schauder fixed-point theorem.Abstract:
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.read more
Citations
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Journal ArticleDOI
Controllability of nonlinear systems in Banach spaces: a survey
TL;DR: A survey on the use of fixed point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces is presented in this article.
Journal ArticleDOI
Controllability of Functional Semilinear Integrodifferential Systems in Banach Spaces
TL;DR: In this article, sufficient conditions for controllability of functional semilinear integrodifferential systems in a Banach space were established by using the Schaefer fixed-point theorem.
Journal ArticleDOI
Controllability of abstract neutral functional differential systems with unbounded delay
TL;DR: By using Sadovskii fixed point theorem, the controllable and the local controllability of abstract neutral functional differential systems with unbounded delay are studied.
Journal ArticleDOI
Controllability of neutral functional differential systems in abstract space
TL;DR: By using fractional power of operators and Sadovskii fixed point theorem, the controllability and the local controllable of abstract neutral functional differential systems with unbounded delay are studied.
Journal ArticleDOI
Existence of solutions and controllability ofnonlinear integrodifferential systems in Banach spaces
K. Balachandran,J. Y. Park +1 more
TL;DR: In this paper, the authors prove the existence of mild and strong solutions of integral differential equations with nonlocal conditions in Banach spaces, using the Schauder fixed-point theorem.
References
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Book
Semigroups of Linear Operators and Applications to Partial Differential Equations
TL;DR: In this article, the authors considered the generation and representation of a generator of C0-Semigroups of Bounded Linear Operators and derived the following properties: 1.1 Generation and Representation.
Journal ArticleDOI
Controllability and Observability in Banach Space with Bounded Operators
TL;DR: In this article, the classical theory of controllability and observability in finite-dimensional spaces is extended to linear abstract systems defined on infinite-dimensional Banach spaces, under the basic assumption that the operator acting on the state be bounded.
Journal ArticleDOI
Existence, stability, and compactness in the -norm for partial functional differential equations
C. C. Travis,Glenn F. Webb +1 more
Journal ArticleDOI
An approach to non-linear control problems using fixed-point methods, degree theory and pseudo-inverses.
M D Quinn,N. Carmichael +1 more
TL;DR: In this article, the authors show how techniques from fixed point and degree theory may be combined with the linear theory of control and observation to create controllability and observability results for a certain class of non-linear systems.