Control problems for discrete Volterra systems

Abstract

In this paper a rigorous Volterra control system theory is developed. In framework of the uniformed view based on operator approach the main control problems such as stability, stabilizability, controllability, linear-quadratic optimization and feedback control problems are considered for linear discrete Volterra equations. It is shown that Volterra operator techniques play a key role to study the main structural properties of the system under consideration. Using the presentation of this operator in the ring of power series allows us to apply some algebraic methods or research.