Application of associated polynomials to circuits and systems.
Stone, Thomas Edward
Parker, Sydney R.
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In this thesis, the theory of associated polynomials is applied to linear circuits and systems. Associated polynomials are defined and used in the presentation of a computer algorithm suitable for accomplishing a partial fraction expansion including repeated roots. Variations of the coefficients of a polynomial are related to the variation of its roots (and vice-versa) by associated polynomials. These results are used in a root solving process and to exoress sensitivity coefficients in; a new analytical form. Lastly , a theory of compensating parameter adjustments is developed with applications to self-adaptive systems. It is shown that by compensating adjustments of any two parameters in the system which are linearly related to the coefficients of the characteristic equation, adaptive compensation is possible for a real root of the closed loop transfer function only and that for complex roots, the real or imaginary parts may be kept invarient but not both.
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