Exponential Stability for a Class of Linear Delay Differential Systems Under Logic Impulsive Control

Abstract

This paper is concerned with the exponential stability for a class of linear delay differential systems under logic impulsive control. Based on logic impulsive control, the strong constraint that the coefficient functions of this kind of linear delay differential system need to be non-negative, which is required in most of the previous studies, is reduced. By establishing the relationship between the logic impulsive system and a corresponding non-impulsive system, some exponential stability criteria for linear delay differential systems under logic impulsive control are presented in the following two cases: Case A–The coefficient functions are non-negative, Case B–The coefficient functions can be negative. Two numerical examples are discussed to verify the results.

Keywords

• Exponential stability
• impulsive control
• logic choice
• linear delay differential system