H∞ Control for Impulsive Disturbances: A State-Space Solution

In this paper we formulate and study an interesting (sub) optimal H∞ control problem related to the attenuation of impulsive disturbances to a class of linear systems. Among the motivating factors is the need to study control problems related to mechanical systems subject to impulsive forces, e.g.active control of the suspension system of a vehicle, accurate pointing of guns, stabilization of an antenna on the space station subject to impact from space debris, or active damping of vibrations of flexible structures caused by impact forces [1,2]. A reasonable control objective in all these problems is to design a stabilizing controller to minimize the induced operator norm from the impulsive disturbances to the controlled outputs. We derive necessary and sufficient conditions for the existence of a (sub) optimal controller, and give a procedure to compute such a controller when one exists