Input–output finite-time stability of discrete-time systems under finite-time boundedness

This paper deals with the input–output finite-time stability of discrete time-varying linear systems in the presence of finite-time boundedness. The state boundedness and output stability of this system are concerned simultaneously to avoid the large unacceptable values during certain transients. For two different classes of norm-bounded input signals, the sufficient conditions for the system satisfying both the state finite-time boundedness (FTB) and input–output finite-time stability (IO-FTS) are developed. Based on a set of linear matrix inequalities (LMIs), the controller design method via state feedback for the discrete-time system satisfying both FTB and IO-FTS is presented for the two classes of external norm-bounded input. The conditions proposed can simultaneously guarantee the state and output of closed-loop system do not exceed the boundary during the specified finite-time interval. Two examples are employed to verify the effectiveness of the proposed method.