Finite Frequency H-/H∞ Stability of Singularly Perturbed Systems

摘要

In this paper, the problem of finite frequency H-/H∞ control for singularly perturbed systems based on GKYP lemma is studied. The objective of the H-/H∞ control problem is to design a controller such that the resulting closed-loop system is stable, and the transfer function is bounded real for singularly perturbed systems at low and high frequencies. By employing GKYP lemma, respectively, on the slow and fast subsystem, the problems of the reduced order subsystems are solved in terms of linear matrix inequalities (LMIs). The two frequency- scale solution for the full-order SPS constructed in this paper uses the solutions of two well-defined lower-order problems, and therefore it is numerically better conditioned. An iterative algorithm for the computation of the BMIs is presented. The effectiveness of the proposed method is demonstrated through comparing with positive real control design method.