Abstract
In this paper, we study robust stability and stabilizability of sampled-data control systems composed of a continuous-time plant and a discrete-time compensator together with sample/hold devices, using the frequency domain method. Our study is not confined only to the case of standard (i.e., single-rate) sampled-data controllers but also extended to the case of multirate sampled-data controllers. Specifically, we compare, by numerical examples, the tolerable amounts of the uncertainty of a given continuous-time plant for which the robust stabilization can be attained in the three cases: the cases of a continuous-time controller, a single-rate sampled-data controller, and a multirate sampled-data controller. The result will be useful for estimating the deterioration caused by use of sampled-data controllers in place of continuous ones, or evaluating the advantages of the multirate sampled-data scheme over the standard one.
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References
M. J. Chen and C. A. Desoer, “Necessary and Sufficient Condition for Robust Stability of Linear Distributed Feedback Systems,” Int. J. Control, Vol. 35, No. 2, pp. 255–267 (1982)
M. Vidyasagar and H. Kimura, “Robust Controllers for Uncertain Linear Multivariable Systems,” Automatica, Vol. 22, No. 1, pp. 85–94 (1986)
A. B. Chammas and C. T. Leondes, “Pole Assignment by Piecewise Constant Output Feedback,” Int. J. Control, Vol. 29, No. 1, pp. 31–38 (1979)
P. T. Kabamba, “Control of Linear Systems Using Generalized Sampled-Data Hold Functions,” IEEE Trans. Automatic Control, Vol. 32, No. 9, pp. 772–783 (1987)
M. Araki and T. Hagiwara, “Pole Assignment by Multirate Sampled-Data Output Feedback,” Int. J. Control, Vol. 44, No. 6, pp. 1661–1673 (1986)
T. Mita, B. C. Pang and K. Z. Liu, “Design of Optimal Strongly Stable Digital Control Systems and Application to Output Feedback Control of Mechanical Systems,” Int. J. Control, Vol. 45, pp. 2071–2082 (1987)
T. Hagiwara and M. Araki, “Design of a Stable State Feedback Controller Based on the Multirate Sampling of the Plant Output,” IEEE Trans. Automatic Control, Vol. 33, No. 9, pp. 812–819 (1988)
M. Araki and T. Hagiwara, “Periodically Time-Varying Controllers,” China-Japan Joint Symposium on Systems Control Theory and Its Application, Hangzhou, China (1989)
M. Araki and K. Yamamoto, “Multivariable Multirate Sampled-Data Systems: State-Space Description, Transfer Characteristics, and Nyquist Criterion,” IEEE Trans. Automatic Control, Vol. AC-31, No. 2, pp. 145–154 (1986)
M. Araki, T. Hagiwara, T. Fujimura and Y. Goto, “On Robust Stability of Multirate Digital Control Systems,” Proc. 29th Conference on Decision and Control, pp. 1923–1924, Honolulu, Hawaii (1990)
C. E. Rohrs, G Stein and K. J. Astrom, “Uncertainty in Sampled Systems,” Proc. American Control Conference, Boston, pp. 95–97 (1985)
S. Hara, M. Nakajima and P. T. Kabamba, “Robust Stabilization in Sampled-Data Control Systems,” Proc. 13th Dynamical System Theory Symposium (in Japanese), pp. 115–120 (1991)
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© 1992 Springer-Verlag
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Araki, M., Hagiwara, T. (1992). Robust stability of sampled data systems. In: Davisson, L.D., et al. Robust Control. Lecture Notes in Control and Information Sciences, vol 183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0114648
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DOI: https://doi.org/10.1007/BFb0114648
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