Bounds for uncertain matrix root-clustering in a union of subregions

✍ Scribed by O. Bachelier; B. Pradin

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 247 KB
• Volume: 9
• Category: Article
• ISSN: 1049-8923
• DOI: 10.1002/(sici)1099-1239(199905)9:6<333::aid-rnc408>3.0.co;2-7

✦ Synopsis

The research for robustness bounds for systems whose behaviour is described by a linear state-space model is addressed. The paper lays stress on the location of the eigenvalues of the state matrix when this matrix is subject either to an unstructured additive uncertainty or to a structured additive uncertainty. In the "rst case, upper bounds on the spectral norm of the uncertainty matrix are determined whereas in the second case, upper bounds on the maximal real perturbation in the state matrix are derived. In both cases, the fact that these bounds are not exceeded ensures that the eigenvalues of the uncertain state matrix lie in a speci"ed region D of the complex plane in which those of the nominal state matrix already lie. These bounds are obtained through a linear matrix inequalities approach. This approach allows to specify D, not only as a simple convex region, symmetric with respect to the real axis, but also as a non-convex (but symmetric with respect to the real axis) region de"ned itself as a union of convex subregions, each of them being not necessarily symmetric with respect to the real axis.