Finite-time boundedness for switched systems subject to both discrete and distributed delays

Abstract

In this paper, the problem of finite-time boundedness of switched systems in the presence of both discrete and distributed delays is addressed. The multiple Lyapunov-Krasovskii functional approach is proposed to give some criteria ensuring that the state trajectories of the system remain bounded within a finite time interval. The switching law is designed in terms of average dwell time technique and the Jensen inequality. To further reduce the conservatism, we adopt the Wirtinger inequality which encompasses the Jensen one to derive a new condition. Finally, two numerical examples are presented to demonstrate the effectiveness of our result and the potential of employing the Wirtinger inequality.

Stability and L1-gain analysis for positive delay systems with large delay period

“…There is plenty of evidence suggesting that when delays happen, problems can develop, causing degradation to the system’s performance and potentially leading the system to an unstable state. Therefore, stability problems have been highlighted in the literature not only for positive systems (Gurvits et al, 2007; Silva–Navarro and Alvarez–Gallegos, 1997; Zhao et al, 2014, 2012), but also for delay systems (Elloumi et al, 2016; Kwon and Park, 2004; Kwon et al, 2014; Liu et al, 2010; Shen and Wang, 2015; Sun et al, 2007; Wang et al, 2015, 2013; Xiang et al, 2012a,b, 2013; Zhu et al, 2012). In Zhu et al (2012), the exponential stability problems of the continuous-time and discrete-time positive systems with constant delay have been addressed by using the Lyapunov–Krasovskii functional method and the asymptotical stability results of positive linear delay systems.…”