Search results for: Lur

Authors: Behzad Moeini Sam, Sara Mohammadi Avandi, Afroz Kianpor

Abstract:

The rituals of fire among the Iranians originate in the general Proto-Indo-European and Indo-Iranian eras when they lived in regions known as the Pontic-Caspian (Indo-Europeans) and Kazakhstan (the Andronovo culture belonging to the Indo-Iranian tribes), and we can get to know about their vulgar heritage despite their separation from each other during several millennia. The early Aryan settlers of Iran had brought their cults to their new home and were bequeathed to them by their Indo-Iranian ancestors. Tradition speaks of several great sacred Iranian fires consecrated by the pre-Zoroastrian kings. Ātar or fire is comparable to the Vedic Agni Atar's functions and elaborately are delineated in the Later Avesta. This paper aims to show the fire cults among the Iranian Lur tribes who originate in the past. Therefore, it will be searched for rituals equally in Indo-European and Indo-Iranian Periods and Old Iranian Texts and their frequency among the Lur tribes. In addition to the library books, we tried to interview the chiefs of Lur tribes. Finally, we concluded that the fire among the Lur Tribes is a sequence of beliefs of the Proto-Indo-European and Indo-Iranian Periods reflected in Old and Middle Iranian texts.

Keywords: Indo-European, Ancient Iran, Fire, Lur, Zoroastrian.

Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

Authors: Xia Zhou, Shouming Zhong

Abstract:

The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.

Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.

Authors: Changchun Shen, Shouming Zhong

Abstract:

This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Lur'e system, linear matrix inequalities, Lyapunov, stability.

Authors: Ju H. Park, S.M. Lee

Abstract:

In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.

Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.