A STUDY OF ASYMPTOTIC STABILITY OF PHASE LOCKED SYSTEMS WITH UNIFORM SAMPLING

Kolgotin Pavel Vyacheslavovich, Engineer, Center of Special Communication and Information, Federal Protective Service of Russia in Penza region, mr_jok@rambler.ru
Kolotkov Alexander Yuryevich, Assistant, sub-department of information security of systems and technologies,
Penza State University, ibst@pnzgu.ru
Doroshkevich Viktor Veniaminovich, Assistant, sub-department of information security of systems and technologies, Penza State University, ibst@pnzgu.ru
Rumyantseva Nina Borisovna, Programmer, sub-department of information security of systems and technologies, Penza State University, ibst@pnzgu.ru
Zefirov Sergey Lvovich, Candidate of engineering sciences, associate professor, head of sub-department
of information security of systems and technologies, Penza State University, ibst@pnzgu.ru
Sultanov Boris Vladimirovich, Doctor of engineering sciences, professor, sub-department of information security of systems and technologies, Penza State University, ibst@pnzgu.ru 

681.511.42 

The article describes a digital phase-locked loop (DPLL) system with even digitization and analog-to-digital convertion to a closed loop of PLL. On the basis of D-decomposition method the authors has defined domains of asymptotic stability of DPLL under consideration. Besides that they have detected a range of values of k1,k2,k3 parameters for which all the roots of characteristic equation of linear approximation of considered discrete nonlinear system are within complex plane unit circumference. 

digital phase-locked loop, mathematical model, asymptotic stability, D-decomposition, transfer function, characteristic equation, singular line, D-curve, domain of stability.