Predictor-Feedback Prescribed-Time Stabilization of LTI Systems With Input Delay

• 成果类型: Article
• 署名作者: Espitia, Nicolas; Perruquetti, Wilfrid
• 署名单位: Universite de Lille; Centre National de la Recherche Scientifique (CNRS); Centrale Lille
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3093527
• 发表日期: 2022
• 页码: 2784-2799
• 关键词: Delays; Linear systems; Backstepping; stability analysis; Time-varying systems; kernel; control design; Backstepping control design; delay systems; infinite-dimensional systems; prescribed-time convergence

摘要

This article first deals with the problem of prescribed-time stability of linear systems without delay. The analysis and design involve the Bell polynomials, the generalized Laguerre polynomials, the Lah numbers, and a suitable polynomial-based Vandermonde matrix. The results can be used to design a new controller-with time-varying gains-ensuring prescribed-time stabilization of controllable linear time-invariant (LTI) systems. The approach leads to similar results compared to Holloway et al. 2019, but offers an alternative and compact control design (especially for the choice of the time-varying gains). Based on the preliminary results for the delay-free case, we then study controllable LTI systems with single input and subject to a constant input delay. We design a predictor feedback with time-varying gains. To achieve this, we model the input delay as a transport partial differential equation (PDE) and build on the cascade PDE-ordinary differential equation setting (inspired by Krstic 2009) so as the design of the prescribed-time predictor feedback is carried out based on the backstepping approach, which makes use of time-varying kernels. We guarantee the bounded invertibility of the backstepping transformation, and we prove that the closed-loop solution converges to the equilibrium in a prescribed time. A simulation example illustrates the results.