Canonical piecewise-linear approximations

Recent Techniques for the Identification of Piecewise Affine and Hybrid Systems

“…To shed some light on the above issues, an experiment is designed with the one-dimensional PWARX system y(k) =f (x(k)) + η(k), and the PWA map f (·) defined as in (18). The additive noise η(k) is normally distributed with zero mean and variance σ 2 η .…”

“…The interest in PWA identification techniques is motivated by several reasons. Since PWA maps have universal approximation properties [18,10], PWA models represent an attractive black-box model structure for nonlinear system identification. In addition, given the equivalence between PWA systems and several classes of hybrid systems [4,14], the many different analysis, synthesis and verification tools for hybrid systems (see, e.g., [2,21,28] and references therein) can be applied to the identified PWA models.…”

Identification of Hybrid Systems A Tutorial

“…The equivalence between PWA models and several classes of hybrid models [4,34,67] makes PWA system identification techniques suitable to obtain hybrid models from data. Moreover, the universal approximation properties of PWA maps [14,49] make PWA models attractive also for nonlinear system identification [64].…”

Estimation of the basin of attractions in CNNs

“…Since finite word-length realizations of digital filters result in systems which inherently are nonlinear, the asymptotic stability of such filters (under zero-input) is of great interest in practice (cf., [1]- [9], [11]- [15], [17] …”