Sampling Bumpless Transfer Control for Multiple Performances of Switched Delay System

Abstract

In this article, a bumpless transfer control (BTC) scheme is developed to mitigate output variations by using sampling input (SI) in switched models subject to interval delay and linear fractional perturbations. Design involving both switching rule (SR) and SI is demonstrated to achieve <inline-formula> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula>, passivity, and <inline-formula> <tex-math notation="LaTeX">${\mathcal {H}}_{2}$ </tex-math></inline-formula> index. Instead of a scheme based on continuous BTC for complicated transfer in switching instant, this proposed one reduces transfer by a simple switching mechanism. The BTC proposed can be further applicable to switched delay model operating under arbitrary switching (ASW). The Zeno behavior of model can be avoided by using the developed BTC with SI and SR. To establish this developed theoretical consequences, a Lyapunov-Krasovskii functional (LKF) with both common and multiple terms is developed. Based on the used full matrix formulation, the developed results can be presented in suitable form which is easy to extend and investigate for more general switched model. Finally, some examples are presented to show our main contribution and practicality of the developed consequences.