Stability analysis for continuous-time switched systems with stochastic switching signals

This paper is concerned with the stability problem of randomly switched systems. By using the probability analysis method, the almost surely globally asymptotical stability and almost surely exponential stability are investigated for switched systems with semi-Markovian switching, Markovian switching and renewal process switching signals, respectively. Two examples are presented to demonstrate the effectiveness of the proposed results, in which an example of consensus of multi-agent systems with nonlinear dynamics is taken into account

Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results

Stability of the supply chain based on disruption classification

Poremećaji mogu uništiti stabilnost opskrbnog lanca što rezultira poslovnim gubitkom, pa je određivanje utjecaja raznih poremećaja na opskrbni lanac značajno. Međutim, postojeće su se analize uglavnom usredotočile na stabilnost opskrbnog lanca u normalnim uvjetima, a istraživale su učinke razine zaliha na stanje sustava i izostavljale utjecaj poremećaja. S nedostatkom analize o karakteristikama poremećaja prilikom modeliranja prebacivog sustava, poremećaji su klasificirani i određeno je vrijeme provedbe svake poremećene razine. Predložena su dvojna pravila prebacivanja s obzirom na dinamiku zaliha i zastoja u isporuci. Izrađen je model prebacivog sustava opskrbnog lanca s višestrukim zastojima. Stabilnost sustava pod različitim razinama poremećaja ispitana je pomoću simulacijske metode. Rezultati pokazuju da se opseg stabilnosti koeficijenata prilagodbe zaliha smanjuje s porastom koeficijenta vremena prijevoza i udaljenosti. Klasifikacija poremećaja ima različite učinke na opskrbni lanac. Pod poremećajem na visokoj razini, razina zaliha proizvodnje značajno se mijenja, a sustav opskrbnog lanca gubi svoju stabilnost i susreće se s poteškoćama u vraćanju na stabilno stanje. Međutim, pod općim poremećajem, sustav opskrbnog lanca postupno se vraća u stabilnost. Sadašnje istraživanje obogaćuje pomaknutu metodu modeliranja opskrbnog lanca i pomaže članovima lanca da učinkovito sprječavaju i reagiraju na poremećaje.Disruptions can destroy the stability of a supply chain resulting in losses in business, thus, determining the influence of various disruptions on a supply chain is significant. However, current studies have mainly concentrated on the stability of a supply chain under normal conditions, exploring the effects of inventory level on the system state and omitting the influences of disruptions. With the lack of analysis on the characteristics of disruption when modelling switched system, disruptions were classified and the lead time of each disruption level was determined. Dual switch rules were proposed considering the stock dynamics and lead time delays. A switched system model of the supply chain with multiple delays was then constructed. System stability under different level disruptions was investigated using simulation method. Results show that the stability scope of inventory adjustment coefficients decreases as transport lead time and distance coefficients increase. Disruption classification has different effects on the supply chain. Under high level disruption, the inventory level of manufacture significantly changes, and the supply chain system loses its stability and encounters difficulty in recovering its stable state. However, under general disruption, the supply chain system recovers to stability gradually. The present exploration enriches the switched modelling method of the supply chain and helps its chain members prevent and respond to disruptions effectively