A Shift Operator Approach to Bilinear System Theory
Arthur E. Frazho · SIAM Journal on Control and Optimization · 1980
Using a transform representation, we present a bilinear realization theory for a Volterra series input–output map. The approach involves the definition of appropriate shift operators on linear spaces associated with the transforms of the kernals in the Volterra series. This approach yields in a very simple manner a theory of minimality and connections with the concepts of span reachability and observability. It also leads to a characterization of finite dimensional realizability in terms of rationality properties of the transforms.