Abstract
Based on the predictor feedback law for the stabilization of discrete-time systems with delay, as introduced in Sect. 1.5, we develop a truncated predictor feedback (TPF) law that simplifies the implementation of its predictor feedback prototype. An eigenstructure assignment based low gain design as well as an alternative Lyapunov equation based design are employed to parameterize the feedback gain matrix of the TPF law in a low gain parameter. The core of low gain feedback designs is that a sufficiently small low gain parameter would compensate an arbitrarily large delay in a discrete-time linear system without exponentially unstable open loop poles.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
K. Gu, “An integral inequality in the stability problem of time-delay systems,” Proc. 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 2805–2810, 2000.
Z. Lin, Low Gain Feedback, London. U.K.: Springer-Verlag, 1998.
Z. Lin, B. M. Chen and X. Liu, Linear Systems Toolkit, Technical Report, Department of Electrical and Computer Engineering, University of Virginia, 2004.
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.
Z. Lin, “On asymptotic stabilizability of discrete-time linear systems with delayed input,” Communications in Information and Systems, Vol. 7, No. 3, pp. 227–264, 2007.
Y. Wei and Z. Lin, “Stabilization of exponentially unstable discrete-time linear systems by truncated predictor feedback,” Systems & Control Letters, Vol. 97, pp. 27–35, 2016.
W. M. Wonham, Linear Multivariable Control: A Geometric Approach, Springer-Verlag, New York, 1979.
B. Zhou, Z. Lin and G. R. Duan, “A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems,” Automatica, Vol. 45, No. 1, pp. 238–244, 2009.
B. Zhou and Z. Lin, “Parametric Lyapunov equation approach to stabilization of discrete-time systems with input delay and saturation,” IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 58, No. 11, pp. 2741–2754, 2011.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Wei, Y., Lin, Z. (2021). 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-53429-5_3
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-53428-8
Online ISBN: 978-3-030-53429-5
eBook Packages: EngineeringEngineering (R0)