&lt;tex&gt;$H_infty$&lt;/tex&gt;Observer Design for Lipschitz Nonlinear Systems

Pertew, A.M.; Marquez, Horacio J.; Zhao, Qing

doi:10.1109/tac.2006.878784

Cited by 155 publications

(86 citation statements)

References 23 publications

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“…It is a highly active research area in academic. Methods based on Lyapunov stability [3][4], H  control [5] [7] and LMI [3][4][6] have been successfully carried out to handle control designs for system with Lipschitz nonlinearity. In previous studies, only Lipschitz nonlinearity of state was considered.…”

Section: Introductionmentioning

confidence: 99%

Control Design for System with Lipschitz Nonlinearity of State Derivative Variables in Reciprocal State Space Form

Tseng¹

2015

Emirates Research Publishing July 8-9, 2015 Singapore

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Section: Introductionmentioning

confidence: 99%

Control Design for System with Lipschitz Nonlinearity of State Derivative Variables in Reciprocal State Space Form

Tseng¹

2015

Emirates Research Publishing July 8-9, 2015 Singapore

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“…However, it is pointed out that this standard problem may have no solution because the regularity assumption is not satisfied. This work is extended in [18] by transforming the problem in order to satisfy the regularity assumption required in the H ∞ optimization.…”

Section: Introductionmentioning

confidence: 99%

Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation

Ichalal

Marx

Mammar

et al. 2012

2012 IEEE International Symposium on Intelligent Control

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To cite this version:Abstract-The problem of observer design for nonlinear Lipschitz systems is dealt with in this work. An emphasis is put on the maximization of the admissible Lipschitz constant for which the observer design is possible. This problem is tackled using a Takagi-Sugeno modeling approach. The idea is to rewrite the state estimation error dynamics as an autonomous Takagi-Sugeno system, using the Mean Value Theorem and the sector nonlinearity transformation. State estimation error dynamics stability is studied with the Lyapunov theory by choosing a non-quadratic Lyapunov function and by computing its variation between m consecutive samples. The interest of these manipulations is to obtain LMI conditions admitting solutions for large values of the Lipschitz constant. Finally, illustrative examples are provided in order to highlight the performances of the proposed approach.

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“…He discussed also the equivalence between the stability condition and the H ∞ minimization in the standard form, and pointed out that this design method was not solvable since the regularity assumptions are not satisfied. Recently, in [19], the result of Rajamani [18] is extended, the authors proposed a dynamic observer and provide a solution to the problem of regularity assumptions by modifying the H ∞ problem. Other classes of nonlinear systems are also studied in the literature to design observers for nonlinear systems, namely Linear Parameter Varying systems (LPV) [3] and bilinear systems.…”

Section: Introductionmentioning

confidence: 99%

Observer design for two-wheeled vehicle: A Takagi-Sugeno approach with unmeasurable premise variables

Ichalal

Arioui

Mammar

2011

2011 19th Mediterranean Conference on Control &Amp; Automation (MED)

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Abstract-This paper is dedicated to the problem of observer design for Takagi-Sugeno (T-S) nonlinear systems with unmeasurable premise variables (TSUPV) and application to autonomous bicycle system. The main idea is based on the use of differential mean value theorem combined to the sector nonlinearity transformation. The objective of this approach is to make the state estimation error dynamic on a T-S form which allows to apply the classical Lyapunov analysis to derive convergence conditions. The design algorithm is proposed in terms of linear matrix inequalities (LMI). To illustrate the proposed methodology, a nonlinear bicycle model is considered.

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<tex>$H_infty$</tex>Observer Design for Lipschitz Nonlinear Systems

Cited by 155 publications

References 23 publications

Control Design for System with Lipschitz Nonlinearity of State Derivative Variables in Reciprocal State Space Form

Control Design for System with Lipschitz Nonlinearity of State Derivative Variables in Reciprocal State Space Form

Observer for Lipschitz nonlinear systems: Mean Value Theorem and sector nonlinearity transformation

Observer design for two-wheeled vehicle: A Takagi-Sugeno approach with unmeasurable premise variables

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