Linear impulsive dynamic systems on time scales
نویسندگان
چکیده
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.
منابع مشابه
First order linear fuzzy dynamic equations on time scales
In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.
متن کاملExistence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales
In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.
متن کاملOn the Φ0-stability of Impulsive Dynamic System on Time Scales
This paper concerns impulsive dynamic system on time scales. We obtain sufficient conditions of the φ0-stability for such systems by employing cone-valued Lyapunov functions.
متن کاملControllability and observability for a class of time-varying impulsive systems on time scales
Abstract. The aim of this paper is to study the controllability and observability for a class of linear time-varying impulsive control systems on time scales. Sufficient and necessary conditions for state controllability and state observability of such systems are established. The corresponding criteria for time-invariant impulsive control systems on time scales are also obtained.
متن کاملHyers-Ulam Stability of Non-Linear Volterra Integro-Delay Dynamic System with Fractional Integrable Impulses on Time Scales
This manuscript presents Hyers-Ulam stability and Hyers--Ulam--Rassias stability results of non-linear Volterra integro--delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem is used for obtaining existence and uniqueness of solutions. By means of abstract Gr"{o}nwall lemma, Gr"{o}nwall's inequality on time scales, we establish Hyers-Ulam stabi...
متن کامل