Recursive control using structure analysis of control systems

In this paper, some operators which denote the systems stabilized by recursive control, are defined. This class of systems is called extended interlaced systems (EIS), and is formed by the compositions of systems with upper-triangular structure and systems with lower-triangular structure. According to the method in this paper, the stabilizing controller of the systems can be constructed easily since the design procedure is constructive and the stabilizing controller can be constructed without complex change of coordinates. What's more, the relation between EIS and fractal is got. From the result, one can understand the systems easily. We can make sure that a system belongs to EIS after analyzing its structure and testing some assumptions.