Fast Stability Analysis for Proportional-Integral Controller in Interval Systems

Abstract

The paper describes a technique for stability analysis of proportional-integral (PI) controller in linear continuous-time interval control systems. The stability conditions of Kharitonov's theorem together with related criterions, such as Routh-Hurwitz criterion for continuous-time systems, bring out sets of polynomial inequalities. The sets are very difficult to solve directly, especially in case of high-order systems. Direct technique was used for stability analysis without solving polynomial inequalities. Solving polynomial equation directly makes its computing speed low. In the paper, a set theory-based technique is proposed for finding robust stability range of PI controller without solving any Kharitonov polynomials directly Computation results confirm expected computing speed of the proposed technique.  This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.