Shift-invariant signal norms for fault detection and control

Two desirable properties of a signal norm to be used for the purpose of optimal control or fault detection are highlighted. These properties are shift-invariance and the permitting of persistent signals. A class of norms, called the window norms, is analyzed. Among norms considered for control purposes, they appear to be the only ones, save the L∞L∞-norm, that satisfy both properties. The signal spaces defined by the window norms, however, include some interesting signals that are not in the L∞L∞-space. The window norms have been found suitable for application in fault detection and are here also considered for optimal control. It is shown that they can be taken as a support for the concept of L1L1-control but may also suggest a new class of optimal controllers.