Robust pole assignment for discrete interval systems

This note presents a method of designing the state feedback gain which places the closed-loop poles of a given discrete interval system inside some region. The Levy-Hadamard and Bendixson theorems have been used to derive algebraic relations which set bounds on the real and imaginary parts of the eigenvalues of the closed-loop system matrix. This helps in placing the closed-loop poles in a specified region, either inside a vertical strip, or inside a horizontal strip, or inside a rectangular region. It turns out that the relations are easily computable and the feedback gain can be determined in a very simple way. A numerical example illustrates the proposed procedure