Abstract
This paper presents a general framework based on lifting technique for sampled-data systems with input time delays. By analyzing the properties of operator-valued matrices of lifted systems with input time delays, an extended lifting technique is obtained. It is then shown that, with the proposed lifting technique, the complex behavior of the system can be illustrated by two simple lifted systems, which construct the extended lifted system. The extended lifted system has the same induced norm as that of the original system with an input time delay, since the proposed lifting technique is an isometric isomorphism. Through applying the proposed lifting technique to sampled-data systems with input time delays, the time-invariant discrete-time system with infinite-dimensional input and output spaces is obtained. The equivalent discrete-time system, which is derived from the extended lifted system, can satisfy the problem of H 2 sampled-data control systems with input time delays. Simulation results are given to show that the proposed method can guarantee a more stable system response than the conventional H 2 sampled-data controller for the sampled-data systems with the various input time delays.
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References
Bamieh, B., Pearson, J. B., Francis B. A., and Tannenbaum, A. 1991. A lifting technique for linear periodic systems with applications to sampled-date control. Systems and Control Letters 17: 79-88.
Bamieh, B. A., and Pearson, J. B. 1992. A general framework for linear periodic systems with applications to H ∞ sampled-data control. IEEE Transactions on Automatic Control 37: 418-435.
Bamieh, B., and Pearson, J. B. 1992. The H 2 problem for sampled-data systems. Systems and Control Letters 19: 1-12.
Chen, T., and Francis, B. A. 1991. H 2-optimal sampled-data control. IEEE Transactions on Automatic Control 36: 387-397.
Chen, T. 1993. A simple derivation of the H 2-optimal sampled-data controllers. Systems and Control Letters 20: 49-56.
Chen, T., and Francis, B. 1995. Optimal Sampled-Data Control Systems. London: Springer-Verlag.
Datko, R. 1993. Two examples of ill-posedness with respect to small time delays in their feedbacks. IEEE Transactions on Automatic Control 38: 163-166.
Dullerud, G., and Lall, S. 1999. Asynchronous hybrid systems with jumps-analysis and synthesis methods. Systems and Control Letters 37: 61-69.
Franklin, G. F., Powell, J. D., and Workman, M. 1997. Digital Control of Dynamic Systems, 3rd edn. Addison Wesley Longman Inc.
Khargonekar, P. P., and Sivashankar, N. 1991. H 2 optimal control for sampled-data systems. Systems and Control Letters 17: 425-436.
Lall, S., and Dullerud, G. 2001. An LMI solution to the robust synthesis problem for multi-rate sampled-data systems. Automatica 37: 1909-1922.
Logemann, H., and Townley, S. 1996. The effect of small delays in the feedback loop on the stability of neutral systems. Systems and Control Letters 27: 267-274.
Marshall, J. E. 1979. Control of Time-Delay systems. London and New York: The Institution of Electrical Engineers.
Nilsson, J. 1998. Real-time control systems with delays. Ph.D. Dissertation, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden.
Qiu, L., and Chen, T. 1994. H 2-optimal design of multirate sampled-data systems. IEEE Transactions on Automatic Control 39: 2506-2511.
Qiu, L., and Chen, T. 1999. Multirate sampled-data systems: All H ∞ suboptimal controllers and the minimum entropy controller. IEEE Transactions on Automatic Control 44: 537-550.
Sheriden, T. B. 1992. Telerobotics, Automation, and Human Supervisory. Cambridge, MA: MIT Press.
Shieh, C. S., Tsai, J. S. H., Shieh, L. S., and Sun, Y. Y. 2001. A genetic approach to hybrid control of sampled-data uncertain systems with input time delay. Computers and Electrical Engineering 27: 395-417.
Toivonen, H. T. 1992. Sampled-data control of continuous-time systems with an H ∞ optimality criterion. Automatica 28: 45-54.
Tsai, C. S., Tsai, M. C., and Sun, Y. Y. 1998. H ∞ sampled-Data control considering computational delays. International Journal of Robust and Nonlinear Control 8: 11-27.
Van Loan, C. F. 1978. Computing integrals involving the matrix exponential. IEEE Transactions on Automatic Control 23: 395-404.
Voulgaris, P. G., Dahleh, M. A., and Valavani, L. S. 1994. H ∞ and H 2 optimal controllers for periodic and multi-rate systems. Automatica 30: 251-263.
Wei, J., and Wenzhong, S. 2001. Controllability of singular systems with control delay. Automatica 37: 1873-1877.
Xiao, L., Hassibi, A., and How, J. P. 2000. Control with random communication delays via a discrete-time jump system approach. In Proceedings of the American Control Conference. Chicago, Illinois, pp. 2199-2204.
Yamamoto, Y. 1990. New approach to sampled-data control systems-A function space method. In Conference on Decision and Control, pp. 1882-1887.
Zhang, W., Branicky, M. S., and Phillips, S. M. 2001. Stability of networked control system. IEEE Control System Magazine (2): 84-99.
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Park, K.S., Park, J.B., Choi, Y.H. et al. Design of H 2 Controllers for Sampled-Data Systems with Input Time Delays. Real-Time Systems 26, 231–260 (2004). https://doi.org/10.1023/B:TIME.0000018245.94136.d0
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DOI: https://doi.org/10.1023/B:TIME.0000018245.94136.d0