On linearizability of strict feedforward systems

Tall, Issa Amadou; Respondek, Witold

doi:10.1109/acc.2008.4586774

Cited by 13 publications

(29 citation statements)

References 16 publications

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“…We will provide an algorithm giving explicit solutions in each case. Recall that we have previously obtained explicit solutions for few subclasses of control-affine systems, namely strict feedforward forms, strict-feedforward nice and feedforward forms, for which linearizing coordinates were found without solving the corresponding PDEs (see [28], [29], [31]). Indeed, for those subclasses we exhibited algorithms that can be performed using a maximum of…”

Section: Nonlinear Systems and Linearization Problemsmentioning

confidence: 99%

“…In this paper we consider general control-affine systems for which we provide a state and a feedback linearizing algorithms that can be implemented each using a maximum of n steps. Those algorithms are, in part, based on the explicit solving of the flow-box theorem [32] and differ completely from those outlined in [28], [31] (see also [18], [19]). Another approach was proposed in [24] based on successive integrations of differential 1-forms.…”

Section: Nonlinear Systems and Linearization Problemsmentioning

confidence: 99%

“…Notice that the algorithm described in [28] allowed only to find (3.1) by computing one component at a time (holding other components identity), starting from ϕ 3 then ϕ 2 and finally ϕ 1 and updating the system after each step. A composition of different coordinates changes gave (3.1).…”

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confidence: 99%

“…Because of the strict feedforward structure, we showed in [28] (using a 4-step algorithm) that the change of coordinates…”

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confidence: 99%

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State and feedback linearizations of single-input control systems

Tall

2010

Systems & Control Letters

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In this paper we address the problem of state (resp. feedback) linearization of nonlinear single-input control systems using state (resp. feedback) coordinate transformations. Although necessary and sufficient geometric conditions have been provided in the early eighties, the problems of finding the state (resp. feedback) linearizing coordinates are subject to solving systems of partial differential equations. We will provide here a solution to the two problems by defining algorithms allowing to compute explicitly the linearizing state (resp. feedback) coordinates for any nonlinear control system that is indeed linearizable (resp. feedback linearizable). Each algorithm is performed using a maximum of n − 1 steps (n being the dimension of the system) and they are made possible by explicitly solving the Flow-box or straightening theorem. We illustrate with several examples borrowed from the literature.

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Section: Nonlinear Systems and Linearization Problemsmentioning

confidence: 99%

Section: Nonlinear Systems and Linearization Problemsmentioning

confidence: 99%

mentioning

confidence: 99%

“…Because of the strict feedforward structure, we showed in [28] (using a 4-step algorithm) that the change of coordinates…”

mentioning

confidence: 99%

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State and feedback linearizations of single-input control systems

Tall

2010

Systems & Control Letters

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“…In a recent paper [22] we completely solved the linearizability for strict feedforward systems. We extend here those results to a special class of feedforward systems.…”

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confidence: 99%

Linearizable feedforward systems: A special class

Tall

2008

2008 IEEE International Conference on Control Applications

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Abstract-We address the problem of linearizability of systems in feedforward form. In a recent paper [22] we completely solved the linearizability for strict feedforward systems. We extend here those results to a special class of feedforward systems. We provide an algorithm, along with explicit transformations, that linearizes the system by change of coordinates when some easily checkable conditions are met. We also re-analyze type II class of linearizable strict feedforward systems provided by Krstic in [9] and we show that this class is the unique linearizable among the class of quasi-linear strict feedforward systems (see Definition III.1). Our results allow an easy computation of the linearizing coordinates and thus provide a stabilizing feedback controller for the original system. They can also be implemented via software like mathematica/matlab/maple using simple integrations, derivations of functions.

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Stabilization by forwarding design for switched feedforward systems with unstable modes

Long

2017

Intl J Robust & Nonlinear

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Summary The problem of global stabilization is investigated for a class of switched nonlinear feedforward systems in this paper where the solvability of the stabilization problem for individual subsystem is not assumed. Some sufficient condition for the stabilization problem to be solvable is derived for the first time by exploiting the multiple Lyapunov functions method and the forwarding technique. Also, we design a switching law and construct bounded state feedback controllers of subsystems explicitly by a recursive design algorithm to achieve global asymptotic stability. The provided technique permits removal of a common restriction in which all subsystems in switched nonlinear feedforward systems are globally asymptotically stable. Finally, a numerical example is provided to demonstrate the feasibility of the theoretical result. Copyright © 2017 John Wiley & Sons, Ltd.

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On linearizability of strict feedforward systems

Cited by 13 publications

References 16 publications

State and feedback linearizations of single-input control systems

State and feedback linearizations of single-input control systems

Linearizable feedforward systems: A special class

Stabilization by forwarding design for switched feedforward systems with unstable modes

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