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. INDEX TERMS Uniform stability; Impulsive differential systems; Impulse time windows; Logic choice; Semi-tensor product; Uncertain.

Stability of Differential Systems with Impulsive Effects

“…This situation changed after the semi-tensor product method was proposed in [100], which can transform logical functions into equivalent algebraic expressions. Against this background, the differential systems with impulses suffered by logic choice have attracted the attention of some researchers in recent years, see [101][102][103][104][105][106][107][108][109].…”

“…In practical applications, impulsive control with impulse time windows may be more effective than impulsive control with fixed times. Until now, stability research on systems with impulse time windows has yielded some results, see [109][110][111][112][113][114][115][116]. For illustration, we cite the following result from [114].…”

“…Recently, a class of uncertain sandwich control system with impulse time windows was proposed in [111], and several exponential stability criteria were obtained in terms of linear matrix inequalities and inequality techniques. In [109], the authors proposed a class of linear (uncertain) delay impulsive differential systems with impulse time windows and logic choice. By using the semi-tensor product method and Lyapunov-Razumikhin technique, some uniform stability criteria were obtained.…”