Optmization for the upper bound of the perturbed parameter in singularly perturbed system based on genetic algorithm

Abstract

A class of linear singularly perturbed system and the optimal problem of the upper bound of the perturbed parameter based on the genetic algorithm are considered. Firstly, the problem of the asymptotically stability is studied in the term of Lyapunov stability theory based on the Linear Matrix Inequality (LMI). Then, the standard problem of the upper perturbed parameter to be optimized is presented. Thirdly, the optimization algorithm for the upper bound of the perturbed parameter in the linear singularly perturbed system is given based on the genetic algorithm. Lastly, two numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed methods.