Controllability of Impulsive Non–Linear Delay Dynamic Systems on Time Scale (original) (raw)

Controllability of semilinear impulsive control systems with multiple time delays in control

IMA Journal of Mathematical Control and Information, 2018

In this article, we study the controllability of finite-dimensional dynamical control systems modelled by semilinear impulsive ordinary differential equations with multiple constant time delays in the control function. Initially, we recall a necessary and sufficient condition for the controllability of the corresponding linear system without impulses, with multiple constant time delays in the control function in terms of a matrix rank condition. Then under some sufficient conditions, we show that the actual system is also controllable for certain classes of non-linearities and impulse functions. We employ Schauder fixed-point theorem and Banach contraction mapping principle to establish the results. Our obtained results are applicable for both autonomous and non-autonomous systems. An example is given to illustrate the theoretical results.

Controllability of time varying semilinear non-instantaneous impulsive systems with delay, and nonlocal conditions

Archives of Control Sciences, 2023

In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously. It is done by using the Rothe's fixed point theorem together with some sub-linear conditions on the nonlinear term, the impulsive functions, and the function describing the nonlocal conditions. Furthermore, a control steering the semilinear system from an initial state to a final state is exhibited.

Approximate controllability of second order impulsive systems with state-dependent delay in Banach spaces

Evolution Equations & Control Theory, 2020

In this paper, we consider the second order semilinear impulsive differential equations with state-dependent delay. First, we consider a linear second order system and establish the approximate controllability result by using a feedback control. Then, we obtain sufficient conditions for the approximate controllability of the considered system in a separable, reflexive Banach space via properties of the resolvent operator and Schauder's fixed point theorem. Finally, we apply our results to investigate the approximate controllability of the impulsive wave equation with state-dependent delay.

On controllability of nonlinear impulsive integrodifferential systems

Many practical systems in physics, chemistry, biology and engineering have impulsive dynamical behaviors due to sudden changes at certain instants during the evolution process. These complex dynamical behaviors can be modeled by impulsive differential equations. This paper studies the exact controllability issue for nonlinear impulsive integrodifferential systems with finite delay in Hilbert spaces. Without imposing compactness condition on the semigroup operator, we establish controllability results by using a fixed point analysis approach. Finally, two examples are provided to show the usefulness of the proposed theory. The results extend and improve some recent results.

Relative controllability of impulsive multi-delay differential systems

Nonlinear Analysis: Modelling and Control

In this paper, relative controllability of impulsive multi-delay differential systems in finite dimensional space are studied. By introducing the impulsive multi-delay Gramian matrix, a necessary and sufficient condition, and the Gramian criteria, for the relative controllability of linear systems is given. Using Krasnoselskii’s fixed point theorem, a sufficient condition for controllability of semilinear systems is obtained. Numerically examples are given to illustrate our theoretically results.

On controllability of second order nonlinear impulsive differential systems

Nonlinear Analysis: Theory, Methods & Applications, 2009

Many dynamical systems in physics, chemistry, biology and engineering sciences have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes. The mathematical models of such processes are called differential systems with impulse effect. This paper studies the exact controllability issue of certain types of second order nonlinear impulsive control differential systems. Sufficient conditions are formulated and proved for the exact controllability of such systems. Without imposing a compactness condition on the cosine family of operators, we establish controllability results by using a fixed point analysis approach. Finally, an example is presented to illustrate the utility of the proposed result. The results improve some recent results.

δ-CONTROLLABILITY OF IMPULSIVE SYSTEMS AND APPLICATIONS TO SOME PHYSICAL AND BIOLOGICAL CONTROL SYSTEMS

International Journal of Differential Equations and Applications Volume 12 No. 3 2013, 171-191 ISSN: 1311-2872 url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijdea.v12i3.1093, 2013

In this paper the conditions for δ-controllability of nonlinear impulsive control systems are investigated using Morales fixed point theorem for strongly accretive maps. The results obtained are applied to impulsive automatic controlled heating and cooling compartments and impulsive control hematopoiesis model. AMS Subject Classification :34A37,93B05,93B52 & 93C95 Key words :controllability,impulsive systems,accretive maps, Morales fixed point theorem and impulsive automatic controller.

Linear impulsive dynamic systems on time scales

Electronic Journal of Qualitative Theory of Differential Equations, 2010

The purpose of this paper is to present the fundamental concepts of the basic theory for linear impulsive systems on time scales. First, we introduce the transition matrix for linear impulsive dynamic systems on time scales and we establish some properties of them. Second, we prove the existence and uniqueness of solutions for linear impulsive dynamic systems on time scales. Also we give some sufficient conditions for the stability of linear impulsive dynamic systems on time scales.

Controllability of fractional noninstantaneous impulsive integrodifferential stochastic delay system

IMA Journal of Mathematical Control and Information, 2021

The paper concerned with the controllability of nonlinear fractional noninstantaneous (NI) impulsive integrodifferential stochastic delay system (ISDS). Some sufficient conditions for the controllability of fractional NI impulsive ISDS have been derived by the new approach of measure of noncompactness in finite dimensional space. This NI impulsive ISDS is more reliable for the evolution process in pharmacotherapy. By using Mönch fixed point theorem, existence results have been proved. The result is new in the finite dimensional setting with NI impulse.

Controllability of linear impulsive systems

Information, Decision and Control , 11-13 Feb. 2002, Adelaide, SA, Australia, IEEE, 2002

Considers controllability properties of linear impulsive dynamical systems. As the controllability of linear impulsive systems is trivial, the investigation is focused on the controllability properties when impulsive vectors are applied in the sub systems of the linear impulsive systems. The controllability conditions including when there is a feedback in the system are derived.