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We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a…

Optimization and Control · Mathematics 2021-07-29 Markus Schöberl , Kurt Schlacher

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

We show that the flatness of a nonlinear discrete-time system can be checked by computing a unique sequence of involutive distributions. The well-known test for static feedback linearizability is included as a special case. Since the…

Optimization and Control · Mathematics 2022-12-29 Bernd Kolar , Johannes Diwold , Markus Schöberl

For discrete-time systems, flatness is usually defined by replacing the time-derivatives of the well-known continuous-time definition by forward-shifts. With this definition, the class of flat systems corresponds exactly to the class of…

Differential Geometry · Mathematics 2021-04-19 Johannes Diwold , Bernd Kolar , Markus Schöberl

It is widely recognized that no tractable necessary and sufficient conditions exist for determining whether a system is, in general, differentially flat. However, specific cases do provide such conditions. For instance, driftless systems…

Optimization and Control · Mathematics 2025-11-11 Jean Lévine , Jaume Franch

In this article, we introduce the notion of differential flatness by pure prolongation: loosely speaking, a system admits this property if, and only if, there exists a pure prolongation of finite order such that the prolonged system is…

Optimization and Control · Mathematics 2024-05-28 Jean Lévine

The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…

Optimization and Control · Mathematics 2018-12-06 Siamak Tafazoli

Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…

Dynamical Systems · Mathematics 2009-11-13 A. J. Roberts

We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite…

Optimization and Control · Mathematics 2015-10-15 Donglei Fan , Danielle C. Tarraf

In the present paper we deal with fully nonlinear two-dimensional smooth control systems with scalar input $\dot{q} = \bs{f}(q,u)$, $q \in M$, $u \in U$, where $M$ and $U$ are differentiable smooth manifolds of respective dimensions two and…

Optimization and Control · Mathematics 2012-06-06 Ulysse Serres

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

This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…

Systems and Control · Electrical Eng. & Systems 2026-04-24 Douglas R. Frey

We show that the Euler-discretization of the nonlinear continuous-time model of a single mast stacker crane is flat. The construction of the flat output is based on a transformation of a subsystem into the linear time-variant discrete-time…

Dynamical Systems · Mathematics 2024-03-26 Johannes Diwold , Bernd Kolar , Markus Schöberl

Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…

Pattern Formation and Solitons · Physics 2020-12-30 Francesco Marino , Giovanni Giacomelli

Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Siegfried Fussy , Gerhard Groessing , Herbert Schwabl

An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…

Quantum Physics · Physics 2019-09-18 Guofeng Zhang , Ian R. Petersen

A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic…

Classical Analysis and ODEs · Mathematics 2019-03-27 Dhurjati Prasad Datta , Soma Sarkar

We derive sufficient conditions for the solvability of the observer design problem for a wide class of nonlinear time-varying systems, including those having triangular structure. We establish that, under weaker assumptions than those…

Optimization and Control · Mathematics 2011-11-03 D. Boskos , J. Tsinias

In this letter, a new notion of stability is introduced, which is called triangular stability. A system is called triangularly stable if the norm of its state vector is bounded by a decreasing linear function of time such that its…

Systems and Control · Electrical Eng. & Systems 2021-04-16 Amir Shakouri , Nima Assadian

Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…

Classical Analysis and ODEs · Mathematics 2009-11-13 Rodica D. Costin