On Flatness of Discrete-time Nonlinear Systems

Kaldmäe, Arvo; Kotta, Ülle

doi:10.3182/20130904-3-fr-2041.00017

Cited by 23 publications

(23 citation statements)

References 10 publications

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“…However, reachability is assumed to hold. As for nonlinear systems, the paper [7] addresses the problem of dynamic feedback linearization. The paper [8] addresses the construction of flat outputs.…”

Section: Introductionmentioning

confidence: 99%

Flatness and Submersivity of Discrete-Time Dynamical Systems

Guillot¹,

Millérioux²

2020

IEEE Control Syst. Lett.

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This paper addresses flatness of discrete-time systems called difference flatness. A definition of flatness, that encompasses the standard ones, in particular backward and forward difference flatness, is introduced. It also allows to cope with systems which are not necessarily controllable or submersive. Besides, it considers nonlinear dynamical systems defined on general sets (without necessary special structures) which can be either continuous or discrete. Based on this definition, a result is established and stipulates that a flat and submersive nonlinear system is fully reachable (which is equivalent to fully controllable). Next, the special case of linear systems is considered leading to a necessary and sufficient condition.

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Section: Introductionmentioning

confidence: 99%

Flatness and Submersivity of Discrete-Time Dynamical Systems

Guillot¹,

Millérioux²

2020

IEEE Control Syst. Lett.

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“…Let us recall that for a given matrix Z, the Moore-Penrose generalized inverse Z † is a matrix of the same dimension as Z so that ZZ † Z = Z, Z † ZZ † = Z † , ZZ † and Z † Z are Hermitian. The matrices P σ(k:k+r) are the dynamical matrices of the left-inverse dynamical system (11).…”

Section: Theorem 1 ([25]mentioning

confidence: 99%

“…When dealing with flatness, we can be interested by at least two different tasks: the construction of flat outputs and the test of flat outputs. As for the first issue, the reader may refer to [1,8,9,10] for LTI discrete-time systems or [11,12,13] for nonlinear discrete-time systems. The other issue amounts to check whether a given output is flat or not.…”

Section: Introductionmentioning

confidence: 99%

Characterization of flat outputs of switched linear discrete-time systems: Algebraic condition and algorithm

Millérioux

Jungers

2021

Systems & Control Letters

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The problem of flat output characterization for switched linear discrete-time systems is addressed. First, an algebraic condition for an output to be flat is provided. It applies for I-flat outputs with the integer I potentially strictly greater than 1. Next, it is proved that such a characterization is decidable. Finally, an efficient algorithm which allows to decide in polynomial time whether a given output is flat is given. The algorithm is built from the observation that the flat output characterization can be expressed in terms of dead-beat stability of an associated constrained switched system. Thus, the notions of joint spectral radius and graph theory play relevant roles in this context.

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“…A recent definition of flatness proposed in Guillot and Millérioux (2020) includes also backwardshifts of the input variables in the flat output. However, within this contribution, similar to Kaldmäe and Kotta (2013), Kolar, Kaldmäe, et al (2016) we restrict ourselves to forward-shifts in the flat output and therefore use the term forward-flatness. The property of forward-flatness is equivalent to linearisability by an endogenous dynamic feedback as proposed in Aranda-Bricaire and Moog (2008).…”

Section: Introductionmentioning

confidence: 99%

A normal form for two-input forward-flat nonlinear discrete-time systems

Diwold

Kolar

Schöberl

2021

International Journal of Systems Science

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We show that every forward-flat nonlinear discrete-time system with two inputs can be transformed into a structurally flat normal form by state-and input transformations. This normal form has a triangular structure and allows to read off the flat output, as well as a systematic construction of the parameterisation of all system variables by the flat output and its forward-shifts. For flat continuous-time systems, no comparable normal form exists.

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On Flatness of Discrete-time Nonlinear Systems

Cited by 23 publications

References 10 publications

Flatness and Submersivity of Discrete-Time Dynamical Systems

Flatness and Submersivity of Discrete-Time Dynamical Systems

Characterization of flat outputs of switched linear discrete-time systems: Algebraic condition and algorithm

A normal form for two-input forward-flat nonlinear discrete-time systems

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