In this paper, a graphical method to analyze the stability of LTI systems, with multiple commensurate time delays, is proposed. It is based on the determination of the purely imaginary roots of the pseudo-polynomial characteristic equation of the system. The proposed technique offers a number of unique features: It allows to have an immediate analysis stability i.e. it allows to verify if the stability of the system is delay-dependent or independent. Also, in the case of delay dependent stability, the method shows immediately all the existing imaginary roots, without solving many equations, as required by analytical methods. Advantages and drawbacks of the method are analyzed in the paper along with some numerical examples.
Graphical method for the stability analysis of commensurate multiple time delay imperfect systems
Xibilia M. G.
2019-01-01
Abstract
In this paper, a graphical method to analyze the stability of LTI systems, with multiple commensurate time delays, is proposed. It is based on the determination of the purely imaginary roots of the pseudo-polynomial characteristic equation of the system. The proposed technique offers a number of unique features: It allows to have an immediate analysis stability i.e. it allows to verify if the stability of the system is delay-dependent or independent. Also, in the case of delay dependent stability, the method shows immediately all the existing imaginary roots, without solving many equations, as required by analytical methods. Advantages and drawbacks of the method are analyzed in the paper along with some numerical examples.Pubblicazioni consigliate
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