Abstract
As with a continuous-time linear system, the predictor state feedback law for a discrete-time linear system with input delay is the product of a feedback gain matrix with the predicted state at a future time instant ahead of the current time instant by the amount of the delay, which is the sum of the zero input solution and the zero state solution of the system. The zero state solution for a discrete-time system is a finite summation that involves past input. The zero input solution is the product of the transition matrix and the initial state. The truncated predictor feedback (TPF), which results from discarding the finite summation part of the predictor feedback law, reduces implementation complexity. The delay independent TPF law further discards the delay-dependent transition matrix in the TPF law and is thus robust to unknown delays. It was pointed out in Lin (Commun. Inf. Syst. 7(3), 227–264 (2007)) and Zhou and Lin (IEEE Trans. Circuits Syst. I Regular Papers 58(11), 2741–2754 (2011)) that such a delay independent TPF law stabilizes a discrete-time linear system with all its poles at z = 1 or inside the unit circle no matter how large the delay is.
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References
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Wei, Y., Lin, Z. (2021). Delay Independent Truncated Predictor Feedback for Discrete-Time Linear Systems. In: Truncated Predictor Based Feedback Designs for Linear Systems with Input Delay. Control Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-53429-5_6
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DOI: https://doi.org/10.1007/978-3-030-53429-5_6
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