A new Lyapunov-like functional approach to dwell-time dependent stability for impulsive systems. Issue 1 (January 2020)

• Record Type: Journal Article
• Authors: Shao, Hanyong; Shao, Lin
• Is Part Of: Journal of the Franklin Institute. Volume 357:Issue 1(2020)
• Page Start: 343
• Page End: 358
• Publication Date: 2020-01
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2019.11.040
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: This paper investigates the dwell-time dependent stability for impulsive systems by employing a new Lyapunov-like functional that is of the second order in time t . In contrary to those built on [ tk, t ], a part of the impulsive interval [ t k, t k + 1 ], the Lyapunov-like functional is two-sided in the sense of employing the system information on [ t, t k + 1 ] as well as [ tk, t ]. To deal with the derivative of the two-sided Lyapunov-like functional, which involves integrals of the state and integrals coupled by [ t, t k + 1 ] and [ tk, t ], integral equations of the impulsive systems are introduced and an advanced inequality is employed. By the Lyapunov-like functional theory, 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 turn out to be less conservative than some existing ones, which is illustrated by numerical examples.