On state covariance bounds for linear stochastic uncertain systems

For the case of robustness of closed-loop linear systems in the face of uncertainty in the system parameters, it is shown that a Riccati equation approach can be pursued in the discrete-time case. The extension requires the analysis of a suitable symplectic pencil. It turns out that, depending on the scalar parameter beta which appears in a H/sub infinity /-type Riccati equation, the picture is more involved than in continuous-time. For some values of beta the stabilizing solution exists but does not yield a covariance bound. The second issue addressed is the problem of computing the value of beta that minimizes the trace of the covariance bound. It is proven that such an optimization problem is convex and therefore amenable to iterative methods of solution.<>