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On the Input-Output Representation of Piecewise Affine State Space Models

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4 Author(s)
Paoletti, S. ; Dipt. di Ing. dell''Inf., Univ. di Siena, Siena, Italy ; Roll, J. ; Garulli, A. ; Vicino, A.

This paper addresses the conversion of discrete-time piecewise affine (PWA) state space models into input-output form. Necessary and sufficient conditions for the existence of equivalent input-output representations of a given PWA state space model are derived. Connections to the observability properties of PWA models are investigated. Under a technical assumption, it is shown that every finite-time observable PWA model admits an equivalent input-output representation. When an equivalent input-output model exists, a constructive procedure is presented to derive its equations. Several examples illustrate the proposed results.

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Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 1 )