Controllability of Nonlinear Systems in Banach Spaces: A Survey

A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces

“…The system (1)-(3) is said to be controllable on the interval I iff, for every x 0 , x b ∈ X, there exists a control u ∈ L 2 (I, U) such that the mild solution x(t) of (1)-(3) satisfies x(0) = x 0 and x(b) = x b [17].…”

“…This concept has been extended to infinite-dimensional spaces by applying semigroup theory [9]. Controllability of nonlinear systems, with different types of nonlinearity, has been studied with the help of fixed point principles [17]. Several authors have studied the problem of controllability of semilinear and nonlinear systems represented by differential and integro-differential equations in finite or infinite dimensional Banach spaces [18][19][20][21].…”

Controllability of Sobolev-Type Neutral Mixed Integrodifferential Evolution System in Banach Spaces

“…Of late the controllability of nonlinear systems in finite-dimensional spaces is studeid by means of fixed point principles [11]. Several authors have extended the concept of controllability to infinite-dimensional spaces by applying semigroup theory [12,13].Controllability of nonlinear systems with different types of nonlinearity has been studied by many authors with the help of fixed point principles [14]. It is remarkable that [15,19,20] provide some sufficient conditions for controllability of integer functional evolution equations of Sobolev type by virtue of semigroup theory via the techniques of fixed point theorem.…”

Controllability of nonlocal impulsive functional integrodifferential evolution systems

“…This concept has been extended to infinite-dimensional spaces by applying semigroup theory ( [19]). Controllability of nonlinear systems with different types of nonlinearity has been studied by many authors with the help of fixed point principles ( [2]). Many systems in physics and biology exhibit impulsive dynamical behavior due to sudden jumps at certain instants in the evolution process.…”