Kharitonov´s theorem and its extensions and applications: An introduction

The objective of this short paper is to briefly introduce the topic area for much of the research to be presented in this invited session. The starting point for this presentation is Kharitonov´s Theorem [1]. A tutorial exposition of Kharitonov´s Theorem will be given and its impact on systems and control will be discussed. This theorem provides neccessary and sufficient conditions for stability of a so-called interval polynomial. More precisely, a family of polynomials of the form p(s)=sn+an-1sn-1+...+a1s+a0 with coefficients ai in prescribed intervals Ai = ??[ai -, ai +] is strictly Hurwitz (all zeros in the strict left half plane) if and only if the 4 polynomials having coefficients an-1 +, an-2 +, an-3 -, an-4 -, an-5 +, an-6 +,... an-1 -, an-2 -, an-3 +, an-4 +, an-5 -, an-6 -,... an-1 +, an-2 -, an-3 -, an-4 +, an-5 +, an-6 -,... an-1 -, an-2 +, an-3 +, an-4 -, an-5 -, an-6 +,... are strictly Hurwitz.