Time maximum disturbance design for stable linear systems: A model predictive scheme

It is known that the most stressful bounded (time maximum) disturbance for stabilized linear systems is of bang-bang type. This bang-bang disturbance can often be implemented with a switch set of current states for second-order systems. The isochrones, as the level sets, determine the value of the disturbance index in a state space setting. In this note, we suggest an efficient way to construct the time maximum disturbance from the information of isochronal wave front using it in a model predictive scheme. This overcomes the shortcomings of the original switch set which are constructed through time backward computation and only available for first and second-order systems. Simulation results show how the isochrones evolve and can be utilized in synthesizing the time maximum disturbance for linear systems of second and then higher order. For third-order systems, the associated L_∞-gain of the time maximizing disturbance is found.