Uniform Stability of Linear Delay Impulsive Differential Systems With Impulse Time Windows and Logic Choice

Abstract

This paper focuses on the uniform stability of linear delay impulsive differential systems with impulse time windows and logic choice. Firstly, a class of linear delay impulsive differential systems with impulse time windows and logic choice is constructed. The impulsive effects of this system have the following two properties: (i) The impulses do not appear at the fixed time points, but may occur at any points in a little range of time. (ii) The impulsive effects are affected by logic choice. Furthermore, by using the semi-tensor product method, we convert the logical functions contained in impulses into equivalent algebraic expressions. Next, based on Lyapunov functions and Razumikhin technique, the uniform stability criterion is obtained. Then, the uniform stability criterion is also applied to a class of linear uncertain delay impulsive differential systems with impulse time windows and logic choice. Finally, two illustrative examples are also discussed.

Keywords

• Uniform stability
• impulsive differential systems
• impulse time windows
• logic choice
• semi-tensor product
• uncertain