Maximal open loop operation under integral error constraints

A linear time invariant system, subjected to bounded parametric uncertainties and time varying disturbances, is to be controlled in open loop for the maximum possible time period. The open loop operation is continued as long as the L₂ norm of the states is bounded by a pre-specified threshold, for every possible value of the uncertainty and disturbance. It is shown that the optimal open loop input that achieves the maximal open loop operation exists and that it can be approximated for computational purposes by a bang-bang input with a finite number of switches. Similarly, the worst case disturbance can also be computed using a bang-bang approximation.