A Generalized KYP Lemma-Based Approach for H∞ Control of Singularly Perturbed Systems

In this paper, H∞ control synthesis of linear time invariant singularly perturbed systems (SPS) based on a generalized KYP lemma approach is investigated. By employing a generalized KYP lemma on the low- and high-frequency domains of SPS, respectively, a slow (low-frequency) controller and a fast (high-frequency) controller are designed to stabilize the slow and fast subsystems, and also to meet the individual H∞ performance specifications. A composite controller for the full-order SPS is constructed via the above two above well-defined lower-order problems. Moreover, the effectiveness of the proposed method is verified as compared with the traditional H∞ design method by its application to a tracking problem of SPS and an H∞ model matching problem for SPS.

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