Transformations into State-Affine Normal Forms

  • Pauline BernardEmail author
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 479)


In this chapter, sufficient conditions on a nonlinear system are given to ensure the existence of a transformation into one of the state-affine normal forms. This includes the linearization by output injection and the nonlinear Luenberger design. The former consists in transforming the system into linear dynamics (possibly depending on the input/output), and such that the output is a linear function of the new state. On the other hand, the latter aims at transforming the system into linear dynamics with a stationary Hurwitz linear part but where the output can be any nonlinear function of the new state. In particular, it is shown that under a rather weak backward distinguishability property, any nonlinear system can be transformed into a Hurwitz linear form in an injective way, but through a time-varying transformation.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi”University of BolognaBolognaItaly

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