Input-output finite-time stabilization with constrained control inputs

In this paper the problem of input-output finite-time stability (IO-FTS) and stabilization of linear time-varying systems is dealt with. The classical definition of IO-FTS is extended to that one of structured IO-FTS, since this allows to incorporate, in the definition of the stabilization problem, some amplitude constraints on the control input variables. A necessary and sufficient condition and a sufficient condition for constrained IO finite-time stabilization are provided in the case of ℒ₂ and ℒ_∞ disturbance inputs, respectively. Such conditions require the existence of a feasible solution to a certain differential linear matrix inequality (DLMI). A numerical example illustrates the effectiveness of the proposed approach.