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

Abstract

This brief focuses on the asynchronous bumpless transfer finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller is constructed, and sufficient conditions are given to ensure the finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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.