Necessary and sufficient conditions for the stability of polynomials with linear parameter dependencies

Abstract

AbstractIn this paper we show that Kharitonov's theorem will provide a necessary and sufficient condition for the stability of a particular family of polynomials where the coefficients are real and linearly dependent on a set of uncertain parameters. The main results are obtained by restricting the linear map from the parameter to the coefficient space to contain the Kharitonov polynomials. The results are applied to both continous‐time and discrete‐time polynomials and future extensions are discussed.