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Extra info for Applications of Time Delay Systems
This choice is motivated by the simplicity of this approach and its relative robustness in the case of constant time-delays. The integration step is chosen to be ﬁxed and equal to the sampling period Ts . The number of steps nk = n(tk ) necessary to estimate the integral at a given . ˆ ˆ k ) and is deﬁned by nk = δk /Ts . This instant t = tk then depends on δˆk = δ(t leads to the following approximation of the integral term, for k = 1, 2, 3, . . 30 E. Witrant et al. ˆ k) tk +δ(t . Ik = I(tk ) = eAtk e−Aθ Bu(θ − τ (θ))dθ, tk nk −1 ≈ Ts e−iATs Bu(k + i − i=0 τ (k + i) ), Ts where the delay is supposed to be a multiple of the sampling period.
IEEE Trans. Automat. Contr. 27(4):869–879 13. Nihtil¨ a M. (1989) Adaptive control of a continuous-time system with time-varying input delay. Systems and Control Letters 12:357–364 On the Use of State Predictors in Networked Control Systems 35 14. Nihtil¨ a M. (1991) Finite pole assignment for systems with time-varying input delays. In Proc. of the 30rd IEEE Int. Conf. on Decision and Control, Brighton, England 15. Nihtil¨ a M. (1991) Pole placement design methodology for input delay systems. In European Control Conference, Grenoble, France 16.
1989) Adaptive control of a continuous-time system with time-varying input delay. Systems and Control Letters 12:357–364 On the Use of State Predictors in Networked Control Systems 35 14. Nihtil¨ a M. (1991) Finite pole assignment for systems with time-varying input delays. In Proc. of the 30rd IEEE Int. Conf. on Decision and Control, Brighton, England 15. Nihtil¨ a M. (1991) Pole placement design methodology for input delay systems. In European Control Conference, Grenoble, France 16. J. (2001) Delay robustness of closed loop ﬁnite assignment for input delay systems.