State space homogenization in hybrid dynamical systems with two subsystems

Abstract

The paper proposes a mathematical framework to be used for the homogenization of the Hybrid Dynamical Systems (HDS) state space. This is based on new mathematical paradigms like non-archimedean valued spaces, p-adic rational numbers and rigid algebraic geometry. Although the mathematical concepts are rather complex we believe the value they bring to solving our problem makes it worthwhile. Here we show how a HDS consisting of two sub-systems could be modeled as a Tate curve, [1]. This paper is a continuation of [2]. We extend and detail here the mathematical framework of embedding a HDS into a Tate curve.