H <sub>∞</sub> control analysis and design for nonlinear systems

Katebi, M.R.; Zhang, Y.

doi:10.1080/00207179508921911

Cited by 25 publications

(8 citation statements)

References 5 publications

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“…We recall in this subsection some results by Katebi and Zhang (1995). See this reference for details.…”

Section: A Su Cient Condition Of Non-oscillationmentioning

confidence: 99%

“…Gray and Nakhla 1981, Katebi and Zhang 1995, Khalil 1992 and references therein). The harmonic linearization method is then classically applied, either for detecting the presence of limit-cycles in the closed loop (this classical nonlinear analysis method has been applied on realistic examples (see e.g.…”

Section: Introductionmentioning

confidence: 97%

“…Because many ¹ tools are already available in Matlab (e.g. in the ¹ Analysis and Synthesis Toolbox, in the Robust Control Toolbox or in the L MI Control Toolbox), our paper (in the same spirit as Katebi and Zhang 1995) has primarily a practical interest, beyond the necessary theoretical justi® cations.…”

Section: Introductionmentioning

confidence: 99%

“…Ferreres and V. Fromion ² Note that the interest of using linear tools (namely H ¥ control, ¹ analysis and ¹ synthesis) in a nonlinear control problem have already been emphasized by Katebi and Zhang (1995) We consider in this section the case of a single SISO nonlinearity. In the ® rst subsection, we ® rst recall a classical graphical method for detecting limit-cycles (without parametric uncertainties).…”

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confidence: 98%

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Nonlinear analysis in the presence of parametric uncertainties

Ferreres¹,

Fromion²

1998

International Journal of Control

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The aim of this paper is to study the existence of limit-cycles in a closed loop, which simultaneously contains nonlinearities and parametric uncertainties. Three methods are presented: we ® rst consider the problem of detecting a limit-cycle using a necessary condition of oscillation. A graphical method and a ® rst ¹ based method are proposed. We then consider the problem of checking the absence of limit-cycles despite parametric uncertainties. A second ¹ based method is proposed, which uses a su cient condition of non-oscillation. An example is ® nally presented: the idea is to use the necessary condition of oscillation, so as to synthesize a controller which modi® es the characteristics (magnitude and frequency) of the limit-cycle.

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“…We recall in this subsection some results by Katebi and Zhang (1995). See this reference for details.…”

Section: A Su Cient Condition Of Non-oscillationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 98%

See 2 more Smart Citations

Nonlinear analysis in the presence of parametric uncertainties

Ferreres¹,

Fromion²

1998

International Journal of Control

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“…The method gives nonconservative results only when the numerator of the LTI element is constant. Katebi and Zhang [7] apply a m-based analysis method to systems with norm-bounded perturbations in the linear part, and incorporate dynamics neglected by the DF method as unstructured uncertainty into the problem description. Tierno [8] fits a rational approximation to the describing function of the nonlinear element, and incorporates describing function analysis into a generalized structured singular value ðmÞ framework of robustness analysis.…”

Section: Introductionmentioning

confidence: 99%

Limit cycle computation for describing function approximable nonlinear systems with box-constrained parametric uncertainties

Nataraj

Barve

2005

Int. J. Robust Nonlinear Control

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SUMMARYWe propose an algorithm to compute the limit cycle set of uncertain non-rational nonlinear systems with nonlinear parametric dependencies. The proposed algorithm computes the limit cycles for a wide class of uncertain nonlinear systems, where the transfer function of the linear element and describing function of the nonlinear element need to be only continuous with respect to the parameters and continuously differentiable with respect to the amplitude and frequency of periodic input signal. The proposed algorithm guarantees that the limit cycles are reliably computed to a prescribed accuracy, and that none of the actual limit cycle point is missed out irrespective of the tightness of the prescribed accuracy. Moreover, for a prescribed accuracy, the proposed algorithm computes all the limit cycles in a finite number of iterations, and an upper bound for this number is also computable. The algorithm is demonstrated on a challenging non-rational example with nonlinear parametric dependencies.

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