Asynchronous Bumpless Transfer Finite-Time H∞ Control for Markovian Jump Systems With Application to Circuit System

This brief focuses on the asynchronous bumpless transfer finite-time
$H_{\infty }$
control problem for a class of Markovian jump systems (MJSs). The hidden Markov principle is introduced to represent the asynchronous jumping phenomenon between the MJSs and the designed bumpless transfer finite-time
$H_{\infty }$
controller. The asynchronous jumping transient behavior of MJSs is described by using a bumpless transfer constraint index. First, an asynchronous bumpless transfer constraint is proposed to limit the control bumps caused by asynchronous jumping. Then, an asynchronous bumpless transfer finite-time
$H_{\infty }$
controller is constructed, and sufficient conditions are given to ensure the finite-time
$H_{\infty }$
performance for MJSs under the proposed asynchronous bumpless transfer method. Finally, an RLC circuit model is provided as an application example to show the effectiveness of the proposed control method.