Extending Kharitonov’s Theorem to More General Sets of Polynomials

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In 1978, a significant new result on the stability of families of polynomials was published by V.L. Kharitonov in Russian [1]. When this result became known in the Western literature, there followed an explosion of results related to Kharitonov’s Theorem; e.g., see [2]–[15]. One of the reasons for the large amount of interest generated by these results is the fact that they provide powerful tools in the design and analysis of control systems which are robust against parameter uncertainty; e.g., see [15]. Indeed, the family of polynomials under consideration is typically the set of all possible characteristic polynomials for a control system containing uncertain parameters. This family of polynomials is generated by mapping the set of allowable uncertain parameters into the set of allowable polynomials coefficients.