Input-output finite-time stabilisation of linear systems with input constraints

In this study, the problem of input-output finite-time stabilisation 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 stabilisation problem, some amplitude constraints on the control input variables. A sufficient condition and a necessary and sufficient condition for structured IO finite-time stabilisation 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. The theory is applied to design the active suspension control system for a two-degree-of-freedom quarter-car model.