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2000•Bulletin of the Korean Mathematical SocietyRequires access

GENERALIZED SOLUTION OF THE DEPENDENT IMPULSIVE CONTROL SYSTEM CORRESPONDING TO VECTOR-VALUED CONTROLS OF BOUNDED VARIATION

Chang-Eon Shin, Ji-Hyun Ryu

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Abstract

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, (i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +, [0,T], x(0)=, where the vector fields f, : are measurable in t and Lipschitz continuous in x, If satisfy a condition that $\forallt_1\; , then the imput-output function can be continuously extended to measurable functions of bounded variation.

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What this paper is about

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, (i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +, [0,T], x(0)=, where the vector fields f, : are measurable in t and Lipschitz continuous in x, If satisfy a condition that $\forallt_1\; , then the imput-output function can be continuously extended to measurable functions of bounded variation.

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Available abstract

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, (i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +, [0,T], x(0)=, where the vector fields f, : are measurable in t and Lipschitz continuous in x, If satisfy a condition that $\forallt_1\; , then the imput-output function can be continuously extended to measurable functions of bounded variation.

Key concepts: Mathematics, Bounded variation, Lipschitz continuity, Bounded function, Vector-valued function, Vector field, Function (biology), Cauchy problem

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