Piecewise linear $ {\rm luz}(\ldots)$ and $ {\rm tar}(\ldots)$ projections. Part 1 – Theoretical background

The paper presents definitions and theorems for $ {\rm luz}(\ldots)$ and $ {\rm tar}(\ldots)$ piecewise linear projections. These projections and their original mathematical apparatus are very useful for modelling of nonlinear systems, eg systems with freeplay or friction.