J. Nonl. Evol. Equ. Appl. 2019 (3), pp. 35-58, published on January 11, 2020:

Stability properties of systems with maximum

S. Dashkovskiy

Institute of Mathematics, University of Würzburg; Emil-Fischer Str. 40, Würzburg 97074, Germany

S. Hristova

Department of Applied Mathematics, Plovdiv University, Tsar Asen st.24, Plovdiv 4000, Bulgaria

K. Sapozhnikova

Institute of Mathematics, University of Würzburg, Emil-Fischer Str. 40, Würzburg 97074, Germany ̈

Received on September 13, 2018, revised version on February 19, 2019
Accepted on February 19, 2019 (with minor revisions)

Communicated by Martin Bohner

Abstract.  In this paper we consider systems of functional differential equations which dynamics depends on the maximum value of solution over a prehistory time interval. Such kind of systems are infinite-dimensional and nonlinear.We consider controlled systems with maximum and study their input-to-state stability property. As well we compare stability properties of such systems with their linear counterparts and it turns out their global stability properties are in many cases better then for the linear counterparts.
Keywords:Infinite-dimensional systems, functional differential equations, input-to-state stability.
2010 Mathematics Subject Classification:   93C23, 93D09.

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