Improvement on stability bounds for singularly perturbed systems via state feedback

Abstract

In this paper, first we give a new characterization for the upper bound ε* of the parasitic parameter ε in singularly perturbed systems, which ensures stability of such systems if 0 < ε < ε*. It will be shown that this upper bound is just the minimum positive eigenvalue of a matrix pair, which can be explicitly constructed from the system matrix. Secondly, based on the new characterization for the stability upper bound, an algorithm for computing this upper bound ε* is established. Thirdly, in order to improve the upper bound ε* via state feedback, an algorithm is developed. Finally, several examples are presented to illustrate the algorithms proposed in this paper.