Control during feedback failure: Characteristics of the optimal solution

The problem of keeping performance errors within bounds while controlling a perturbed open loop linear system is considered. The objective is to maximize the time during which performance errors remain acceptable, given that the controlled system is within a specified neighborhood of its nominal parameter values. It is shown that the optimal solution is associated with a switching function z(t) which has the following feature: the optimal input signal is a bang-bang signal when z(t) is not the zero function.