Dwell-time-dependent stability results for impulsive systems

作者：Shao, Hanyong^*; Zhao, Jianrong

来源：IET Control Theory and Applications, 2017, 11(7): 1034-1040.

DOI：10.1049/iet-cta.2016.1350

• stability
• Lyapunov methods
• functional equations
• integral equations
• time-varying systems
• sampled data systems
• periodic impulses
• aperiodic impulses
• impulsive system stability
• time-varying Lyapunov-like functional approach
• cross-terms
• integral states
• impulsive states
• tight bounds
• improved Jensen inequality
• integral equation
• dwell-time-dependent stability
• maximal dwell-time
• minimal dwell-time
• periodic impulsive systems
• aperiodic impulsive systems

This study is concerned with the dwell-time stability for impulsive systems under periodic or aperiodic impulses. A Lyapunov-like functional approach is established to study the stability for impulsive systems. The Lyapunov-like functional is time-varying and decreasing but is not imposed definite positive nor continuous. A specific Lyapunov-like functional is constructed by introducing the integral of state together with the cross-terms of the integral and impulsive states. A tight bounding is obtained for the derivative of this functional with the help of the improved Jensen inequality reported recently and the integral equation of the impulsive system. On the basis of the Lyapunov-like functional approach, new dwell-time-dependent stability results with ranged dwell-time, maximal dwell-time and minimal dwell-time are derived for periodic or aperiodic impulsive systems. The stability results have less conservatism than some existing ones, which are illustrated by numerical examples.

• 出版日期2017-4-25
• 单位曲阜师范大学