Bumpless Transfer Hybrid Non-Fragile Finite-Time Control for Markovian Jump Systems and its Application

Abstract

In this article, the issue of bumpless transfer hybrid non-fragile 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 for Markovian jump systems (MJSs) is investigated, where the transition rates are partially available. The non-fragile strategy with tolerating both additive and multiplicative perturbations is designed, which greatly relaxes the application scope of the traditional controller. The bumpless transfer control idea is introduced to depict the transient behavior caused by a jumping controller. First, a bumpless transfer constraint condition is provided to restrict the amplitude of the hybrid non-fragile jumping controller, for which the additive and multiplicative perturbations are considered. Then, a bumpless transfer hybrid non-fragile controller is developed to guarantee the solvability of 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> control issue for MJSs with partially available transition rates. Finally, an electronic circuit system example is applied to illustrate the usefulness of the proposed bumpless transfer hybrid non-fragile control approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the finite-time hybrid non-fragile <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 issue of MJSs with the bump limitation constraint. The bumpless transfer is often encountered in the Markovian jumping control field because it is usually impossible to implement unlimited control signals or bumpy control signals and is a main source of instability, and degradation of performance of MJSs. The traditional bumpless transfer technique because of the constant control gain cannot handle effectively the non-fragile bumpless transfer problem for MJSs. In this paper, the restriction of the constant control gain is relaxed. We develop a bumpless transfer control strategy considering a strong non-fragility of the control gain. In contrast to the existing results, a non-fragile bumpless transfer can tolerate the co-existing additive and multiplicative perturbations with a wider application. This study presents the method for practitioners interested in bumpless transfer controller design.

Topics & Concepts