Frequency-restricted norm bounds for interval systems

We investigate bounds of frequency-restricted norms (FRN), a generalization of H∞-norm, for SISO LTI interval systems, where the numerator and the denominator are interval polynomials. Though the H∞-norm of interval systems can be determined by 16 Kharitonov-type systems, we can show that this fact is not true in general by a counterexample. A special class of systems for which the FRN is bounded by fixed extremal systems is derived. On the basis of this result, an example of PI-type controller design considering both parametric and unstructured perturbations is illustrated by a parameter space design method.