Abstract
The truncated predictor feedback design simplifies the predictor feedback design by discarding the distributed delay term . The implementation of the remaining static feedback term of the predictor feedback law requires the exact knowledge of the input delay. The truncated predictor state feedback law for continuous-time linear systems with a constant delay is such an example. The exact value of the delay appears in the exponential factor eAτ of the truncated predictor feedback law. Moreover, the determination of the value of the feedback parameter of the truncated predictor feedback law requires, although not the exact value of the delay, an upper bound of the delay to be known. This requirement of the information of the delay, which explicitly or implicitly appears in the truncated predictor feedback law, suggests that the truncated predictor feedback law is delay-dependent. The delay-dependency of the truncated predictor feedback law also manifests itself in the observer based feedback design. To construct an observer whose state asymptotically approaches the state of the open loop system, the dynamics of the observer generally contains the delayed input. This implies that the exact value of the delay is also required in the construction of the observer used in the observer based truncated predictor feedback law.
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References
N. Bekiaris-Liberis and M. Krstic, “Stability of predictor-based feedback for nonlinear systems with distributed input delay,” Automatica, Vol. 70, pp. 195–203, 2016.
N. Bekiaris-Liberis and M. Krstic, “Predictor-feedback stabilization of multi-input nonlinear systems,” IEEE Transactions on Automatic Control, Vol. 62, No. 2, pp. 516–531, 2017.
R. Bellman and K. L. Cooke, Differential-Difference Equations, New York: Academic, 1963.
D. Bresch-Pietri and M. Krstic, “Adaptive trajectory tracking despite unknown input delay and plant parameters,” Automatica, Vol. 45, No. 9, pp. 2074–2081, 2009.
D. Bresch-Pietri and M. Krstic, “Delay-adaptive predictor feedback for systems with unknown long actuator delay,” IEEE Transactions on Automatic Control, Vol. 55, No. 9, pp. 2106–2112, 2010.
K. L. Cooke and Z. Grossman, “Discrete delay, distributed delay and stability switches,” Journal of Mathematical Analysis and Applications, Vol. 86, No. 2, pp. 592–627, 1982.
M. Krstic, Delay Compensation for Nonlinear, Adaptive, and PDE Systems, Boston: Birkhäuser, 2009.
Z. Lin, Low Gain Feedback, London. U.K.: Springer-Verlag, 1998.
Z. Lin and H. Fang, “On asymptotic stabilizability of linear systems with delayed input,” IEEE Transactions on Automatic Control, Vol. 52, No. 6, pp. 998–1013, 2007.
M. S. Mahmoud, Robust Control and Filtering for Time-delay Systems, CRC Press, 2000.
D. Tsubakino, M. Krstic and T. R. Oliveira, “Exact predictor feedbacks for multi-input LTI systems with distinct input delays,” Automatica, Vol. 71, pp. 143–150, 2016.
Y. Wei and Z. Lin, “Maximum delay bounds of linear systems under delay independent truncated predictor feedback,” Automatica, Vol. 83, pp. 65–72, 2017.
Y. Wei and Z. Lin, “A delay-independent output feedback for linear systems with time-varying input delay,” International Journal of Robust and Nonlinear Control, Vol. 28, No. 8, pp. 2950–2960, 2018.
Y. Wei and Z. Lin, “Time-varying low gain feedback for linear systems with unknown input delay,” Systems & Control Letters, Vol. 123, pp. 98–107, 2019.
B. Zhou, G. Duan and Z. Lin, “A parametric Lyapunov equation approach to the design of low gain feedback,” IEEE Transactions on Automatic Control, Vol. 53, No. 6, pp. 1548–1554, 2008.
B. Zhou, Z. Lin and G. Duan, “Properties of the parametric Lyapunov equation based low gain design with application in stabilizing of time-delay systems,” IEEE Transactions on Automatic Control, Vol. 54, No. 7, pp. 1698–1704, 2009.
B. Zhou, Z. Lin and G. Duan, “Truncated predictor feedback for linear systems with long time-varying input delays,” Automatica, Vol. 48, No. 10, pp. 2387–2399, 2012.
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Wei, Y., Lin, Z. (2021). Delay Independent Truncated Predictor Feedback for Continuous-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_5
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DOI: https://doi.org/10.1007/978-3-030-53429-5_5
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