A finite-time generalized H2 gain measure and its performance criterion

In this paper, the performance measure problem is considered for a linear time-varying system with non-zero initials and bounded external disturbance in a finite-time horizon. A finite-time generalized H₂ gain is proposed which is defined as a ratio of the maximal penalty output and the sum of the energy of the exogenous input and nonzero initial conditions in a finite time interval. The finite-time generalized H₂ gain proposed can be used as a performance metric of such a class of systems in the worst-case which are not required to be stable and with zero initials. We proved several properties of the proposed finite-time generalized H₂ gain and its performance criterion is also proved. The computation of the finite-time generalized H₂ gain is then treated. We also provide an application and simulation results of the proposed finite-time generalized H₂ gain measure.