On Robust Stabilization in the Gap Metric for LTV Systems

In this paper, we consider the robust stabilization problem for linear time varying systems using the gap metric. In particular, we show that the time varying (TV) directed gap reduces to the computation of an operator with a TV Hankel plus Toeplitz structure. Computation of the norm of such an operator can be carried out using an iterative scheme similar to the standard two-block H^infin problem. The infimization in the TV directed gap formula is shown to be a minimum by using duality theory. The latter holds as well in the time-invariant case