Input-output finite time stabilization of linear systems

In this paper the problem of input-output finite-time stabilization of linear time-varying systems is dealt with. The classical definition of input-output finite-time stability (IO-FTS) is extended to that one of structured IO-FTS, which allows to incorporate, in the definition of the stabilization problem, some amplitude constraints on the control input variables. A sufficient condition and a necessary and sufficient condition for structured IO finite-time stabilization are provided in the case of L∞ and L2 inputs, respectively. Such conditions require the existence of a solution to a certain differential linear matrix inequality (DLMI). The theory is applied to design the active suspension control system for a two-degree-of-freedom quarter-car model.