Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Stability Analysis of Volterra Type Functional Equations by the Method of Realization

Author(s):

Yulia Alexandrovna Abdalova

Faculty of Mathematics and Mechanics,
St. Petersburg State University. Universitetskaya nab. 7/9,
St. Petersburg, 199034 Russia

yuliannia@gmail.com

Volker Reitmann

70 corp.3, Botanicheskaya st,
Peterhof, Saint-Petersburg,
198516, Russia
Saint-Petersburg State University
professor of the Department of Applied Cybernetics
Prof. Dr.

vreitmann@aol.com

Abstract:

Methods of realization of input-output operators by abstract discrete-time control systems and frequency method are used for the stability and instability analysis of a class of nonlinear Volterra type functional equations. The key idea is to consider a time-discrete invariant control system generated by an abstract map in some weighted functional spaces. Evolution equations with impulse-amplitude modulation which generate typical discrete-time control systems are considered. A brief description of Yakubovich’s abstract stability method for discrete-time nonlinear control system used in the present paper is given.

Keywords

• discrete-time system
• input-output operator
• realization method
• Volterra functional equation

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