Time domain characterization of finite frequency properties via behavioral approach

Many of practical design specifications are provided by finite frequency properties described by inequalities over restricted finite frequency intervals. A quadratic differential form (QDF) is a useful algebraic tool when we consider the dissipation theory based on the behavioral approach. In this paper, we consider a time domain characterization of the finite frequency domain inequalities (FFDIs) using QDFs. We first derive an LMI condition which is equivalent to the FFDIs. Using the condition, we derive a time domain characterization of the FFDIs in terms of QDFs as a main result of this paper. This condition recovers the previous result in the sense that our result can characterize the FFDIs for the system of nonproper transfer functions.