Computational Complexity of Kharitonov’s Robust Stability Test

Owing to several uncertainties in the modelling of a system, checking for “robust stability” is, in fact, a more practical goal for any designer. In this, instead of a single matrix A, a family of matrices (A + δA) has to be checked for negative definiteness. This led us to the question “How long does a computer take to check the sign definiteness of a family of matrices?” Mathematically, we still have a system of d ifferential equations, but each of the coefficients belongs to certain interval, g iving rise to “families of polynomials”. The family of polynomials must be tested to be certain that all the roots lie in the left half of the complex plane. We simply consider the 4 bounding polynomials of Kharitonov and run the algorithms developed above 4 times. Ev idently, the savings in computational time is huge. This paper exp lores the computationally faster algorithm to determine the robust stability of an interval of polynomials.