Abstract
It is shown that the principle of the argument is the basis for the different stability criteria for linear continuous and discrete systems. From the principle of argument stability criteria in the frequency domain are derived which lead to Hermite-Bieler theorems for continuous and discrete systems. Routh-Hurwitz criterion and its equivalent for discrete systems, Schur-Cohn criterion and its equivalent for continuous systems are directly obtained. Moreover, the monotony of the argument for different functions can be proved using Hermite-Bieler theorem. Using the principle of the argument and the continuity of the roots of a polynomial w.r.t. its coefficients, all known robust stability results can be obtained in a straightforward and simple way.
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References
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© 1992 Springer-Verlag
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Mansour, M. (1992). The principle of the argument and its application to the stability and robust stability problems. In: Davisson, L.D., et al. Robust Control. Lecture Notes in Control and Information Sciences, vol 183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0114644
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DOI: https://doi.org/10.1007/BFb0114644
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