Stability tests for singular cases of discrete systems (Q582257)

This paper deals with stability tests for discrete systems \(x(k+1)=Ax(k)+Bu(k)\) with the characteristic equation \[ (*)\quad f(z)=| zI-A| =b_ 0z^ n+...+b_ n=0. \] Some numerical array can be constructed, starting from the coefficients \(b_ 0,...,b_ n\). The number of positive and negative elements in the first column of the array is connected to the number of roots of (*) inside the unit circle. This paper is devoted to the analysis of some singular situations, where some elements in the first column vanish.