A two-operator approach to robust stabilization of linear systems on.

Robust non-fragile feedback stabilization is studied for causal linear time-invariant (LTI) input–output systems defined in an L 2 () signal space setup, or equivalently in an L 2 (j) setup in the frequency domain. Two-operator descriptions for the plant and the controller are used with bounded operators defined on the full space L 2 (). Basic properties of causal LTI operators on weighted L 2 spaces, L 2 (,   w ), which are relevant to stabilization theory, are also established for different choices of the weighting function w . Weighted L 2 spaces allow the inclusion of persistent signals such as steps and thus provide the potential of important generalizations of the robust stabilization theory on L 2 (). In particular, it is shown that there is a large class of weights w for which the L 2 (,   w ) setup leads to H ∞ optimization. This implies that robust H ∞ design can be applied to a large class of weighted L 2 spaces on . Problems of closability of unstable causal LTI convolution operators are discussed. This strengthens the importance of the two-operator model Ay   =   Bu as the basic plant input–output model on the full time axis. It is discussed how to obtain such models with A and B bounded causal coprime operators defined on the full signal space. [ABSTRACT FROM AUTHOR]