Complete Controllability of Impulsive Stochastic Integrodifferential Systems in Hilbert Space

Abstract

This paper concerns the complete controllability of the impulsive stochastic integrodifferential systems in Hilbert space. Based on the semigroup theory and Burkholder-Davis-Gundy's inequality, sufficient conditions of the complete controllability for impulsive stochastic integro-differential systems are established by using the Banach fixed point theorem. An example for the stochastic wave equation with impulsive effects is presented to illustrate the utility of the proposed result.

Banach fixed-point theorem in semilinear controllability problems – a survey

“…Theorem 6 [79]. Suppose that Hypotheses 15-18 are satisfied and the operator Φ is a contraction mapping from H 2 to H 2 , and has a unique fixed point.…”

“…In [79], authors consider the complete controllability of following impulsive stochastic integro-differential systems in a Hilbert space:…”

“…theorem about complete controllability using the Banach fixedpoint theorem, we have to introduce the next lemma and a few hypotheses [79]. Lemma 1.…”

“…the theorem about complete controllability using the Banach fixedpoint theorem, we have to introduce a few hypotheses [79,80]. It should be pointed out that Hypotheses 20-22 are the simpler form of the Hypotheses 15-17.…”

Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint

“…Exhaustive work has been made in this field. See, for instance, [26][27][28][29][30][33][34][35][36][37][38][39] and references therein. Related studies are of interest, for instance, in synchronization, deterministic, and stochastic stabilization, impulsive vaccination in epidemic models, control of chemical process under their various dynamics, and so forth.…”