Dwell-Time-Dependent ${H_\infty }$ Bumpless Transfer Control for Discrete-Time Switched Interval Type-2 Fuzzy Systems
Siyuan Zhang, Jun Zhao
Abstract
This article investigates the <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> bumpless transfer control problem for a class of discrete-time switched interval type-2 (IT2) fuzzy systems subject to dwell-time constraint. We proposed a novel description of bumpless transfer performance for discrete-time switched IT2 fuzzy systems. With the aid of the dwell-time-dependent Lyapunov function approach and a novel mixed switching strategy, sufficient conditions ensuring the asymptotic stability with an <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> bumpless transfer performance are derived. More incisively, the bumpless transfer performance in this article is only required over the subintervals of the active interval, which is more general and relaxes the limitation of traditional bumpless transfer performance in the existing results. Besides, dwell-time-dependent bumpless transfer IT2 fuzzy controllers are designed in the form of linear matrix inequalities. Finally, a single-link robot arm model is employed to demonstrate the potential and effectiveness of the derived theoretical results.