Some classical number sequences in control system design

Algebraic tools of LTI control systems design need graphical and analytical structures which depend on dimension of their control parameter space. Essential elements for optimal low-order control systems are the least stable system poles, i.e. the rightmost on the complex plane characteristic roots. Their mutual location is described by critical root diagrams; the algebraic design procedure uses the root polynomials, i.e. factors of characteristic polynomials, which involve only the rightmost poles. From a theoretical point of view it is important to know the dependence between control space dimension and numbers of arising object sets and their asymptotics; they are represented by Fibonacci numbers and partial sums of Euler partitions. From a practical design point of view we need complete lists of required diagrams and polynomials; so we specify the recursive procedure to build a root polynomial list for each control parameter dimension.