H2 control with time domain constraints

We study the problem of minimizing the H₂ norm of a given transfer function subject to time-domain constraints on the time response of a different transfer function to a given test signal. The main result of the paper shows that this problem admits a minimizing solution in H₂. Moreover, rational solutions with performance arbitrarily close to optimal can be found by constructing a family of approximating problems. Each one of these problems entails solving a finite-dimensional quadratic programming problem whose dimension can be determined before hand