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Non-fragile PD state ${H}_{\infty }$ control for a class of uncertain descriptor systems. (English) Zbl 1245.93045
Summary: This paper is concerned with the problem of non-fragile proportional-plus-derivative (PD) state ${H}_{\infty }$ control for a class of uncertain descriptor systems. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in the state matrix but also in the derivative matrix. A new version of bounded real lemma for descriptor systems is proposed, which guarantees a descriptor system to be normal and stable (NS) with $\gamma$-disturbance rejection. Based on this, we address the problem of designing non-fragile PD state ${H}_{\infty }$ controllers with additive and multiplicative controller uncertainties, respectively. Sufficient conditions are presented to synthesize two classes of such non-fragile controllers in terms of LMIs. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design method.
##### MSC:
 93B36 ${H}^{\infty }$-control 93B52 Feedback control