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Related papers: A Flat System Possessing no (x,u)-Flat Output

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We consider flat differential control systems for which there exist flat outputs that are part of the state variables and study them using Jacobi bound. We introduce a notion of saddle Jacobi bound for an ordinary differential system of $n$…

Optimization and Control · Mathematics 2024-04-01 Yirmeyahu J. Kaminski , François Ollivier

Consider the controlled system $dx/dt = Ax + \alpha(t)Bu$ where the pair $(A,B)$ is stabilizable and $\alpha(t)$ takes values in $[0,1]$ and is persistently exciting, i.e., there exist two positive constants $\mu,T$ such that, for every…

Optimization and Control · Mathematics 2016-08-14 Antoine Chaillet , Yacine Chitour , Antonio Loría , Mario Sigalotti

The suggestion of writing, for some problems, nonlinear state equations not as dx/dt = F(x,u,t), but as dx/dt = [A(t,x)]x + [B(t,x)]u(t), which is more "constructive", is considered supported by arguments related to: the axiomatization of…

Exactly Solvable and Integrable Systems · Physics 2008-10-24 Emanuel Gluskin

This paper is devoted to normal forms for x-flat control-affine systems with two inputs. We propose a general triangular normal form which contains several other normal forms discussed in the literature as special cases. We derive…

Dynamical Systems · Mathematics 2024-11-05 Conrad Gstöttner , Bernd Kolar , Markus Schöberl

This paper proposes a tracking controller based on the concept of flat inputs and a dynamic compensator. Flat inputs represent a dual approach to flat outputs. In contrast to conventional flatness-based control design, the regulated output…

Systems and Control · Computer Science 2012-11-27 Jean-Francois Stumper , Ferdinand Svaricek , Ralph Kennel

Despite ongoing research, testing the flatness of discrete-time systems remains a challenging problem. To date, only the property of forward-flatness - a special case of difference-flatness - can be checked in a computationally efficient…

Optimization and Control · Mathematics 2026-02-10 Johannes Schrotshamer , Bernd Kolar , Markus Schöberl

Let's consider a control system described by the implicit equation $F(x,\dot x) = 0$. If this system is differentially flat, then the following criterion is satisfied : For some integer $r$, there exists a function $\varphi(y_0, y_1,…

Optimization and Control · Mathematics 2017-11-15 Bruno Sauvalle

We propose an algorithmic test to check whether a two-input system is linearizable by an endogenous dynamic feedback with a dimension of at most two. This test furthermore provides a procedure for systematically deriving flat outputs for…

Dynamical Systems · Mathematics 2023-01-11 Conrad Gstöttner , Bernd Kolar , Markus Schöberl

Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…

Dynamical Systems · Mathematics 2015-05-29 xiwei Liu , Tianping Chen

We introduce a task-relative taxonomy of actuator inputs for nonlinear systems within the input-output feedback-linearization framework. Given a flat output specifying the task, inputs are classified as essential, redundant, or dexterity:…

Systems and Control · Electrical Eng. & Systems 2026-03-10 Mirko Mizzoni , Pieter van Goor , Barbara Bazzana , Antonio Franchi

This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each…

Systems and Control · Electrical Eng. & Systems 2023-12-12 Hao Yin , Bayu Jayawardhana , Stephan Trenn

Recently it has been shown that the property of forward-flatness for discrete-time systems, which is a generalization of static feedback linearizability and a special case of a more general concept of flatness, can be checked by two…

Optimization and Control · Mathematics 2025-12-23 Johannes Schrotshamer , Bernd Kolar , Markus Schöberl

We introduce a new definition of $\pi$-flatness for linear differential delay systems with time-varying coefficients. We characterize $\pi$- and $\pi$-0-flat outputs and provide an algorithm to efficiently compute such outputs. We present…

Optimization and Control · Mathematics 2014-09-30 F. Antritter , F. Cazaurang , J. Lévine , J. Middeke

We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.

Dynamical Systems · Mathematics 2013-07-03 Vahid Bokharaie , Oliver Mason

This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and twocontrols. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems…

Optimization and Control · Mathematics 2011-12-14 David Avanessoff , Jean-Baptiste Pomet

This chapter presents an approach to embed the input/state/output constraints in a unified manner into the trajectory design for differentially flat systems. To that purpose, we specialize the flat outputs (or the reference trajectories) as…

Systems and Control · Electrical Eng. & Systems 2020-11-12 Maria Bekcheva

In this paper, we present a structurally flat triangular form which is based on the extended chained form. We provide necessary and sufficient conditions for an affine input system with two inputs to be static feedback equivalent to the…

Dynamical Systems · Mathematics 2021-07-29 Conrad Gstöttner , Bernd Kolar , Markus Schöberl

This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a…

Optimization and Control · Mathematics 2016-11-17 Daniel Liberzon , A. Stephen Morse , Eduardo D. Sontag

It is well known that for flat systems the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovsk\'y state are…

Optimization and Control · Mathematics 2024-08-01 Conrad Gstöttner , Bernd Kolar , Markus Schöberl

In this paper a class of simple, but nonlinear, systems of recursions involving $2$ dependent variables $x_{j}\left( n\right) $ is identified, such that the solutions of their initial-values problems -- with arbitrary initial data…

Exactly Solvable and Integrable Systems · Physics 2024-07-29 Francesco Calogero