Zhou, Rongxing Synthesis and analysis of a feedback control system. (English) Zbl 0802.93019 Syst. Sci. Math. Sci. 6, No. 4, 312-319 (1993). For detection of the modulating signals \(x_ 1\) and \(x_ 2\) in the frequency modulated and multiplicatively coupled signal \(v(t)= A_ 1\cdot\sin(\omega_ 1 t+ x_ 1(t))\cdot A_ 2\cdot\sin(\omega_ 2 t+ x_ 2(t))\), a cross-coupled phase-locked loop with multiplication, abbreviated \(CCPLL(M)\), is proposed. In the paper, for a first-order loop the global structural stability analysis is carried out, and the acquisition and synchronization regions are obtained. For the second- order loop, the synchronization region is calculated, too. Reviewer: A.Munack (Braunschweig) MSC: 93B50 Synthesis problems 93B52 Feedback control 94A14 Modulation and demodulation in information and communication theory 93C10 Nonlinear systems in control theory 93D15 Stabilization of systems by feedback Keywords:detection; modulating signals; cross-coupled phase-locked loop; global structural stability PDFBibTeX XMLCite \textit{R. Zhou}, Syst. Sci. Math. Sci. 6, No. 4, 312--319 (1993; Zbl 0802.93019)