SICE Journal of Control, Measurement, and System Integration
Online ISSN : 1884-9970
Print ISSN : 1882-4889
ISSN-L : 1882-4889
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Robustification of a Nonlinear Dynamical System with a Stability Index and a Matrix Inequality
Yasuaki OISHIMio KOBAYASHITetsuya YOSHINAGA
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2015 Volume 8 Issue 3 Pages 209-213

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Abstract

A problem in the field of nonlinear dynamics is considered with a technique of control theory. In particular, for preventing a nonlinear dynamical system from making undesirable bifurcation, it is proposed to control its parameter with a stability index and a matrix inequality. A basic idea is to update the parameter of the system so as to minimize the stability index. Since the stability index is not differentiable as a function of the parameter, its minimization is carried out through equivalent transformation to a smooth minimization problem, where a matrix inequality is used. The proposed method is applied to a simple dynamical system and shown to be effective. Its generalization is also considered for driving a system to avoid chaos.

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© 2015 The Society of Instrument and Control Engineers
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