Abstract
This paper deals with the linear quadratic regulation problems for the linear discrete-time systems with l input delays. The design of the optimal control law is transformed into solving one Diophantine equation and one spectral factorization with delays. A new and simple approach for the spectral factorization is proposed based on reorganized innovation analysis. The calculation of spectral factor comes down to solving l + 1 Riccati equations with the same dimension as the original systems.
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Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Jae Weon Choi. This work was supported by the Nature Science Foundation of Shandong Province under grant Y2008G04 and Y2007G34 and National Science Foundation for Distinguished Young Scholars of P.R. China under grant 60825304, and 60804034.
Hong-Guo Zhao received his Ph.D. degree in Control Theory and Control Engineering from Shandong University, P.R. China, in 2008. He joined Taishan University in 2008 and his research interests cover Kalman filtering, optimal control and time delay systems.
Huan-Shui Zhang received his Ph.D. degree in Northeast University, P.R. China, in 1997. His research interests include robust filtering, optimal control, and signal processing.
Peng Cui received his Ph.D. degree in Control Theory and Control Engineering from Shandong University, P.R. China, in 2008. He joined Shandong University in 2008 and his current research interests include state estimation, optimal control and networked control systems.
Xiao Lu received his Ph.D. degree from Dalian University of Technology, P.R. China, in 2008. Currently, he joined Shandong University of Science and Technology, and his research interests include robust filtering and control, and time delay systems.
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Zhao, HG., Zhang, HS., Cui, P. et al. Spectral factorization for multiple input delayed discrete-time systems with applications to control. Int. J. Control Autom. Syst. 8, 662–666 (2010). https://doi.org/10.1007/s12555-010-0320-7
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DOI: https://doi.org/10.1007/s12555-010-0320-7