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Insensitive output feedback $$H_{\infty}$$ control of delta operator systems with insensitivity to sampling time jitter. (English) Zbl 1284.93091
Summary: The insensitive multi-objective $$H_{\infty}$$ control synthesis problem via dynamic output feedback for linear delta operator systems with insensitivity to sampling time jitter is investigated in the case of small sampling times. The delta-domain model instead of the standard shift-domain model is used to avoid the inherent numerical ill-condition resulting from using the latter model at high sampling rates. Parameter sensitivity function of the transfer function with respect to sampling time is defined to mitigate the effect of sampling time jitter because it may cause significant degradation of the overall system performance. It is worth pointing out that a novel bounded real lemma for delta operator allowing extra degree of freedom for multi-objective control design is presented by using the well-known projection lemma. Then, from this new lemma, a two-step design procedure based on LMI is presented to design insensitive dynamic output feedback controllers such that the resulting closed-loop system is asymptotically stable and meets the requirement of sensitivity specification. A numerical example is also presented to show the effectiveness of the proposed method.

##### MSC:
 93B36 $$H^\infty$$-control 93B35 Sensitivity (robustness) 93B52 Feedback control 93B50 Synthesis problems 93D20 Asymptotic stability in control theory
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