Robust pole-clustering for descriptor systems a strict LMI characterization

This paper tackles the problem of the characterization of robust pole-clustering for descriptor systems using linear matrix inequalities (LMI). It states a necessary and sufficient condition for a descriptor system to be impulse free and to have its finite poles in a specified convex region of the complex plane. A sufficient condition to guarantee this result in the presence of norm-bounded uncertainties is established. The results are expressed in terms of strict LMIs, thus they are numerically tractable with LMI optimization tools. Numerical examples are given.