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

Author

Paoletti, Simone ; Roll, Jacob ; Garulli, Andrea ; Vicino, Antonio

Author_Institution

Dipt. di Ing. dell´´Inf., Univ. di Siena, Siena, Italy

Volume

55

Issue

1

fYear

2010

Firstpage

60

Lastpage

73

Abstract

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.

Keywords

discrete time systems; nonlinear control systems; observability; piecewise linear techniques; state-space methods; PWA model; discrete-time piecewise affine state space models; finite-time observable properties; input-output representations; Controllability; Equations; Jacobian matrices; Nonlinear dynamical systems; Nonlinear systems; Observability; Region 1; State-space methods; Sufficient conditions; System identification; Observability; piecewise affine (PWA) models; realization theory; state-space and input-output representations;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2034224

Filename

5350420