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Article

Biák, Martin ; Janovská, Drahoslava
Differential algebraic equations of Filippov type. (English). In: Brandts, J., Korotov, S., Křížek, M., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Application of Mathematics 2015, In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Proceedings. Prague, November 18-21, 2015. Institute of Mathematics CAS, Prague, 2015. pp. 1-16
MSC: 34C60, 37N30, 65P30 | Zbl 06669915
Keywords:
Filippov systems; differential algebraic equations (DAEs); Filippov systems with DAEs; soft drink process
Summary:
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.
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