Stability criterion for continuous-time system polynomials with uncertain complex coefficients

An alternative and simple derivation for Kharitonov´s theorem for both the complex and the real cases is provided. The approach is based on extensions to complex polynomials of certain properties associated with Hurwitz polynomials that are well known for the real case in the context of passive network theory. First, the characteristic lossless positive real (LPR) complex rational functions are defined. Next, they are associated with (complex) Hurwitz polynomials. Based on these mathematical preliminaries, Kharitonov´s stability criterion for uncertain complex polynomials is derived. The special form of the criterion for real polynomials is also considered