Robust stabilizing solution of the Riccati difference equation

The control law for infinite horizon H(2) control of linear discrete-systems with norm bounded time-varying uncertainties has been presented in the literature. In this paper, a sufficient condition for robust stability of this control is presented. Based upon the results obtained, a connection is made between the monotonic behavior of the Riccati difference equation (RDE) and the robust stability of "frozen" closed-loop systems. This connection then allows the derivation of a robust stability condition for "frozen" closed-loop systems, which depends only on the initial condition of the RDE. An example is included to illustrate the implementation of the proposed theory.