Robust pole region placement for linear structured uncertain systems

This paper presents a method of designing the state feedback which place the closed-loop poles of a given uncertain system inside some region. The Lévy-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 state feedback can be determined in a very simple way. A numerical example illustrates the proposed procedure.