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This letter concerns the Schur stability of convex combinations of complex polynomials. For given two Schur stable complex polynomials, a sufficient condition is given such that the convex combination of polynomials is also Schur stable.
In many engineering problems it is required to convert a polynomial into another polynomial through a transformation. Due to its wide range of applications, the polynomial transformation has received much attention and many techniques have been developed to compute the coefficients of a transformed polynomial from those of an original polynomial. In this letter a new result is presented concerning the transformation matrix for arbitrary polynomial transformation. A simple algorithm is obtained which enables one to successively compute transformation matrices of various order.