Sentence examples for systems with orders from inspiring English sources

The work proves that precise control of atoms to create a transistor smaller than any other quantum system available is possible and opens the door to further research into harnessing these tiny transistors for computers and systems with orders of magnitude more processing power than today's machines.

Meanwhile, it was shown that chaos existed in fractional-order financial systems with orders less than three and period doubling and intermittency routes to chaos in the fractional-order financial system were found.

This paper is concerned with observer-based stabilization for fractional-order descriptor systems with order 1≤α<2.

We have further given the asymptotic stability results of the perturbed systems with order.

Especially, the fractional differential systems with order have recently gained an increasing attention [23, 28 31].

In Section 3, the stability analysis is presented for autonomous linear fractional differential systems with order.

Then, some literatures on the stability of linear fractional differential systems with order have been appeared [11 15].

Hence, the stability of linear fractional differential systems with order has also been considered by using the conversion methods and transfer function [8, 10].

In addition, this paper mainly focuses on the case that the fractional order is (0<alpha<2), since there exists an equivalent relation of fractional-order systems with order (0 <andhaleq1) and with order (1leqbeta< 2); see [15].

In this paper, we study the stability of autonomous linear fractional differential systems, nonautonomous linear fractional differential systems, and the corresponding perturbed systems with order by using the properties of Mittag-Leffler functions and the Gronwall inequality.

For the autonomous linear fractional differential systems with order, the necessary and sufficient conditions on stability and asymptotic stability are given, which are almost the same as those with the fractional derivative order.