On time scaling for nonlinear systems: Application to linearization

Sampei, Mitsuji; Furuta, K.

doi:10.1109/tac.1986.1104290

Cited by 128 publications

(57 citation statements)

References 2 publications

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“…The resulting differential equations would be more directly related to the system dynamics but would be complicated in general. A similar issue arises with feedback linearization in [11,Eqn. (22)] where a significant number of necessary conditions are given for the TSF.…”

Section: Remark 35mentioning

confidence: 88%

“…PROBLEM STATEMENT Early work on time scaling for control design [11], [12], [13] enlarged the class of state feedback linearizable systems. To generalize the class of single-output systems which admits an OF, an output dependent time scaling transformation was introduced in [8]:τ = s(y(t)) > 0, τ (t 0 ) = τ 0 , where s(y(t)) is a non-vanishing positive smooth function, called a time scale function (TSF).…”

Section: Introductionmentioning

confidence: 99%

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Time scaling of a multi-output observer form

Wang

Lynch

2008

2008 American Control Conference

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Time scalings in the multi-output observer form for uncontrolled nonlinear continuous-time systems are considered in this paper. It is the multi-output version of an existing single-input result. Time scaling broadens the class of systems which admits an exact error linearization observer design by including time scaling transformations. The existence conditions of the time scaling transformation and the change of state coordinates to time-scaled observer form are provided. IEEE Transactions on Automatic ControlThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved.

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Section: Remark 35mentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Time scaling of a multi-output observer form

Wang

Lynch

2008

2008 American Control Conference

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“…The time-scaling scheme proposed by Sampei and Furuta (Sampei & Furuta, 1986) depends on the state of the system …”

Section: The Time-scaling Conceptmentioning

confidence: 99%

Time-scaling in the Control of Mechatronic Systems

Kiss¹,

Szadeczky-Kardoss²

2008

New Developments in Robotics Automation and Control

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“…As a consequence, beginning with the pioneering works of Krener [24] and Brockett [3], up to the present time there has been increasing interest in the various modifications of the exact linearization problem. Survey of this field can be found in papers [16,31] or in books [22,29].In spite of being aware that all these surveys do not cover many important subfields like time-scaling transformations [33] or dynamic feedback [7,8], this paper does not aim to give an updated survey of the overall linearization area. It will be concentrated only on the global aspects of the exact linearization since a systematic and self-contained exposition on this topic is still missing.…”

mentioning

confidence: 99%

“…In spite of being aware that all these surveys do not cover many important subfields like time-scaling transformations [33] or dynamic feedback [7,8], this paper does not aim to give an updated survey of the overall linearization area. It will be concentrated only on the global aspects of the exact linearization since a systematic and self-contained exposition on this topic is still missing.…”

mentioning

confidence: 99%

Global linearization of nonlinear systems - A survey

Čelikovský

1995

Banach Center Publ.

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Abstract.A survey of the global linearization problem is presented. Known results are divided into two groups: results for general affine nonlinear systems and for bilinear systems. In the latter case stronger results are available. A comparision of various linearizing transformations is performed. Numerous illustrative examples are included.1. Introduction. Exact linearization of nonlinear control systems is probably the most intensively studied and best understood area of the differential geometric approach to the nonlinear control. It presents a natural and challenging task: to find suitable compensations that make a given nonlinear system to behave in a linear fashion, or at least closely to it. This problem deserves a lot of attention: its positive solution directly extends the applicability of the linear methods to a more general nonlinear class of systems. As a consequence, beginning with the pioneering works of Krener [24] and Brockett [3], up to the present time there has been increasing interest in the various modifications of the exact linearization problem. Survey of this field can be found in papers [16,31] or in books [22,29].In spite of being aware that all these surveys do not cover many important subfields like time-scaling transformations [33] or dynamic feedback [7,8], this paper does not aim to give an updated survey of the overall linearization area. It will be concentrated only on the global aspects of the exact linearization since a systematic and self-contained exposition on this topic is still missing.The number of results on global linearization is rather modest in comparision with the above mentioned linearization boom. The main reason for this is that

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On time scaling for nonlinear systems: Application to linearization

Cited by 128 publications

References 2 publications

Time scaling of a multi-output observer form

Time scaling of a multi-output observer form

Time-scaling in the Control of Mechatronic Systems

Global linearization of nonlinear systems - A survey

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