1,721,005 research outputs found
A remark about linear switched systems in the plane
No full textIn this note we prove that if a switched system F formed by a pair of linear vector fields of R2 is asymptotically controllable, then the discrete time operator associated to F admits at least one real eigenvalue p, with |p| < 1. For the particular case at hand, this is an improvement of previous existing results
C'era una volta il regolo calcolatore
No full textIn questo articolo si racconta brevemente la storia del regolo calcolatore e del concetto matematico che e' alla base del suo funzionamento: i logaritm
Disegnare con le equazioni
No full textSistemi di equazioni differenziali ordinarie sono spesso usati in matematica per simulare leggi fisiche sperimentali. Nel caso di sistemi di due equazioni in due incognite, le soluzioni possono essere rappresentate come famiglie di curve che riempiono il piano; esse formano un disegno, detto ritratto delle fasi. Osservando le proprieta' geometriche di queste curve e la forma del disegno, e' possibile ricavare informazioni sull'evoluzione del fenomeno modellizzato. Con questo articolo, ci si propone di mostrare come certi ritratti di fase possano essere tracciati sullo schermo di un computer facendo uso di un software appropriato. Cio' permette di scoprire proprieta' matematiche interessanti della dinamica dei sistemi, senza trascurare gli aspetti estetici dei disegni
Stability of Switched Systems: An IntroductionLarge-Scale Scientific Computing
No full textIn this note we review some problems typically encountered in the theory of stability of switched systems. Moreover, we present some recent achievements on this subjec
The Mechanism of Plana's Calendar
Full text linkTo menage complex social activities such as job, religion, commerce, political institutions, the mankind needs to develop tools for measuring and organizing time. Roughly speaking, such tools are clocks (for period of time less than one day) and calendars (for periods longer than a day). Since the most ancient civilized countries, calendar modeling has been related to the periodic motion of celestial bodies. Of course, from the Earth's point of view, the most important celestial bodies are the Sun and the Moon. Unfortunately, the periods of their motions are difficult to compare, and cannot be reduced each other easily. Other merely cultural traditions (for instance, the 7 days week) further complicate thinks. In summary, to design a calendar is not an easy task. This may not be a problem as far as we operate over short periods, small areas, and the amount of the required information is minimal. But the amount of information and the need of precision becomes more and more crucial, because of the evolution of the human society and the growth of complexity
Stabilization by means of state space depending switching rules
No full textIn this paper we consider switched systems defined by a pair of linear systems , , such that there exists a neutrally stable linear combination of the matrices , . Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense. The result is illustrated by some simulations and examples
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