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On generalized Popov theory for delay systems. (English) Zbl 1249.93141
Summary: This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoryless state feedback control law which guarantees the (exponential) closed-loop stability with an \(\mathcal L_2\) norm bound constraint on disturbance attenuation. Note that the proposed results extend similar ones proposed by some of the authors [V. Ionescu et al., Automatica 37, No. 1, 91–97 (2001; Zbl 0965.93083)].

MSC:
93D10 Popov-type stability of feedback systems
93B52 Feedback control
93C05 Linear systems in control theory
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