A time domain characterization of finite frequency properties for multi-dimensional behaviors

Many of practical design specifications are provided by finite frequency properties described by inequalities over restricted finite frequency intervals. In this paper, we consider a time domain characterization of the finite frequency domain inequalities (FFDIs) for multi-dimensional behaviors using quadratic differential forms (QDFs), which are useful algebraic tools for the dissipation theory based on the behavioral approach. Based on QDFs, result, we derive a characterization of the FFDIs using the compensating rate which guarantees the dissipativity of some behavior with some rate constraints as a main result. This is a generalization of previous works for one-dimensional systems to the multi-dimensional case.