A generalized canonical piecewise-linear representation

Explicit formulas for the solutions of piecewise linear networks

“…In a similar way the expression for can be obtained (10) Note that many electrical PL networks are class-P networks [2]- [4], [11]. Exceptions are, for instance, networks with hysteretic behavior.…”

“…Note also that and, therefore, a link does exist to the explicit model descriptions, e.g., the ones proposed by Chua. Chua's model descriptions are normally expressed using the absolute-value operator [2]- [4].…”

“…However, the values and might be chosen such that holds. According to the definitions of the ideal diode, it follows immediately that and, hence, Consequently, using (4) can be expressed as…”

“…For these PL-models, various formulations or model descriptions have been devised [2]- [4]. However, it has recently been shown that they all are special cases of a so-called state-model description [5].…”

Linear Approximation of Continuous Systems with Trapezoid Step Functions

“…There exists an extensive literature about PWL functions, since they played an important role in approximation, regression and classification. One of the biggest problems concerns their explicit representation in a closed form [9,20]. Another important issue is to find a PWL approximation of a certain function in order to minimize or bound the overall area (or the distance in each point) between the original function and the approximation [8,19,21].…”