H∞ bumpless transfer control for switched affine systems with its application to turbofan engine model

Switched affine systems (SASs) are a special class of switched systems. The existing works about SASs predominantly focuses on steady-state performance. There exist limited attention given to transient performance, particularly the transient performance induced by switchings. The inappropriate switchings can induce severe signal jumps, degrade the steady-state performance of the system, and even lead to instability. The bumpless transfer control (BTC) represents an effective strategy for mitigating signal jumps. However, the existing BTC methods are primarily designed for general switched systems, and these approaches are often not applicable to SASs. This article is focussed on the issue of $ H_{\infty } $ H∞ BTC for SASs under unmodeled disturbances. Firstly, an affine term (AT) related to $ H_{\infty } $ H∞ bumpless transfer (BT) performance definition is introduced for the SAS to characterise the alleviation level of the bumps in the control input signal at switching points. Secondly, a criterion is established to enable the solvability of the $ H_{\infty } $ H∞ BTC problem for the SAS. Thirdly, an $ H_{\infty } $ H∞ BT controller and a switching signal are co-designed to drive the SAS to satisfy the $ H_{\infty } $ H∞ BT performance which may not be shared by the subsystems. Finally, a turbofan engine model example is implemented to illustrate the availability and rationality of the suggested $ H_{\infty } $ H∞ BTC scheme.