We will study discontinuous dynamical systems of Filippov-type. Mathematically, Filippov-type systems are defined as a set of first-order differential equations with discontinuous right-hand side. These systems arise in various applications, e.g. in control theory (so called relay feedback systems), in chemical engineering (an ideal gas--liquid system), or in biology (predator-prey models). We will show the way how to extend these models by a set of algebraic equations and then study the resulting system of differential-algebraic equations. All MATLAB simulations are performed in modified version of the program developed by Petri T. Piiroinen and Yuri A. Kuznetsov published in ACM Trans. Math. Software, 2008.
@article{702961,
title = {Differential algebraic equations of Filippov type},
booktitle = {Application of Mathematics 2015},
series = {GDML\_Books},
publisher = {Institute of Mathematics CAS},
address = {Prague},
year = {2015},
pages = {1-16},
zbl = {06669915},
url = {http://dml.mathdoc.fr/item/702961}
}
Biák, Martin; Janovská, Drahoslava. Differential algebraic equations of Filippov type, dans Application of Mathematics 2015, GDML_Books, (2015), pp. 1-16. http://gdmltest.u-ga.fr/item/702961/