On Practical Input-Output Finite-Time Stability Based on Principle of Self-Support

In this paper, based on the principle of self-support (PSS) and an existing definition of input-output finite-time stability (IO-FTS), a totally new concept which is defined as practical input-output finite-time stability (PIO-FTS) is proposed. First, the concept of PSS is reviewed and a theorem about tracking in the practical sense is listed by virtue of robotic system. Second, two different design algorithms for controller gain are presented to illustrate the effectiveness of the PSS. Finally, by introducing the existing definition of the IO-FTS, which is used to quantify the input-output behavior of the dynamics within a prescribed finite time interval, a framework about combining the PSS with IO-FTS is given to guarantee the approximate asymptotic tracking of control systems in a finite time.