The H∞ control problem for linear time-varying systems

The authors consider the standard problem of H^∞ control theory for finite-dimensional linear time-varying continuous-time plants: given a real number γ>0, find (if one exists) an internally stabilizing controller such that the closed-loop operator norm is less than than γ. Under the weak assumptions on the plant model, it is shown that a solution to this problem exists if and only if a pair of matrix Riccati differential equations admits positive-semidefinite stabilizing solutions. Also state-space formulae for one solution to the problem are given