2014 Volume 7 Issue 2 Pages 112-121
Many of practical design specifications are provided by finite frequency properties described by inequalities over restricted finite frequency intervals. In this paper, the authors consider a characterization of the finite frequency domain inequalities (FFDIs) for n-dimensional systems from a view point of a dissipation theory using quadratic differential forms (QDFs), which are useful algebraic tools for the dissipation theory based on the behavioral approach. The QDFs allow us to derive a clear characterization of the FFDIs using some inequality analogous to dissipation inequality with a compensation rate and an inequality of an integral of the supply rate with a matrix integral quadratic constraint as a main result. This characterization leads to a physical interpretation in terms of the dissipativity for subbehavior with some rate constraints. The authors also show how to resolve a difficulty on the expression of a compensation rate peculiar to n-dimensional systems. The results of this paper can be regarded as a finite frequency version for the characterizations of frequency properties over the entire frequency domain due to Pillai and Willems (2002).