Robust asymptotic stability of linear time-varying uncertain system with respect to its state mean

This paper studies a novel kind of robust stability, namely robust asymptotic stability with respect to states' means, of linear time-varying (LTV) uncertain systems. Roughly speaking, the system will feature this robust stability if its state variables' mean values gradually approach to their equilibrium states. Robust input-output finite-time stability (IO-FTS) of the LTV uncertain system over a bounded time interval is first introduced; however, it may suffer steady-state error due to modeling uncertainties. This gives rise to a demand for the stability robustness analysis corresponding to such uncertainties by studying the averaging system behavior focusing on the steady-state error rejection. Furthermore, a case study is provided to endorse significant superiority of our work.