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The finite inclusions theorem

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2 Author(s)
Kaminsky, R.D. ; Digital Storage Div., Shrewsbury, MA, USA ; Djaferis, T.E.

This paper presents a novel necessary and sufficient condition for a polynomial to have all its roots in an arbitrary convex region of the complex plane. The condition may be described as a variant of Nyquist's stability theorem; however, unlike this theorem it only requires knowledge of the polynomial's value at finitely many points along the region's boundary. A useful corollary, the finite inclusions theorem (FIT), provides a simple sufficient condition for a family of polynomials to have its roots in a given convex region. Since FIT only requires knowledge of the family's value set at finitely many points along the region's boundary, this corollary provides a new convenient tool for the analysis and synthesis of robust controllers for parametrically uncertain systems

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Automatic Control, IEEE Transactions on  (Volume:40 ,  Issue: 3 )