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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2021

Predictor-feedback prescribed-time stabilization of LTI systems with input delay

Résumé

This paper deals first 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 polynomialbased Vandermonde matrix. The results can be used to design a new controller-with time-varying gains-ensuring prescribedtime stabilization of controllable LTI systems. The approach leads to similar results compared to Holloway et al. 2019 but offers an alternative and compact control design (specially 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 PDE and build on the cascade PDE-ODE 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 timevarying 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.
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Dates et versions

hal-03275335 , version 1 (01-07-2021)

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Nicolás Espitia, Wilfrid Perruquetti. Predictor-feedback prescribed-time stabilization of LTI systems with input delay. IEEE Transactions on Automatic Control, In press, ⟨10.1109/TAC.2021.3093527⟩. ⟨hal-03275335⟩
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