Robust Kalman Filter Synthesis for Uncertain Multiple Time-Delay Stochastic Systems
Tóm tắt
The problem of robust Kalman filter synthesis is considered in this present study for discrete multiple time-delay stochastic systems with parametric and noise uncertainties. A discrete multiple time-delay uncertain stochastic system can be transformed into another uncertain stochastic system with no delay by properly defining state variables. Minimax theory and Bellman-Gronwall lemma are employed on the basis of the upper norm-bounds of parametric uncertainties and noise uncertainties. A robust criterion can consequently be derived which guarantees the asymptotic stability of the uncertain stochastic system. Designed procedures are finally elaborated upon with an illustrative example.
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Tài liệu tham khảo
Alford R. L. , and LeeE. B., 1986, “Sampled Data Hereditary Systems: Linear Quadratic Theory,” IEEE Trans. Automat. Control, Vol. 31, pp. 60–65.
Feliachi A. , and ThowsenA., 1981, “Memoryless Stabilization of Linear Delay-Differential Systems,” IEEE Trans. Automat. Control, Vol. 26, pp. 586–587.
Wang S. S. , ChenB. S., and LinT. P., 1987, “Robust Stability of Uncertain Time-Delay Systems,” Internat. J. Control, Vol. 46, pp. 963–976.
Ikeda M. , and AshidaT., 1979, “Stabilization of Linear Systems with Time-Varying Delay,” IEEE Trans. Automat. Control, Vol. 24, pp. 369–370.
Chou J. H. , HorngI. R., and ChenB. S., 1989, “Dynamical Feedback Compensator for Uncertain Time-Delay Systems Containing Saturating Actuator,” Internal. J. Control, Vol. 49, pp. 961–968.
Mori T. , 1985, “Criteria for Asymptotic Stability of Linear Time Delay Systems,” IEEE Trans. Automat. Control, Vol. 30, pp. 158–161.
Mori T. , FukumaN., and KuwaharaM., 1981, “Simple Stability Criteria for Single and Composite Linear Systems with Time Delays,” Internal J. Control, Vol. 34, pp. 1175–1184.
Patel N. K. , DasP. C., and PrabhuS. S., 1982, “Optimal Control of Systems Described by Delay Differential Equations,” Internat. J. Control, Vol. 36, pp. 303–311.
Hsiao F. H. , HsiehJ. G., and WuM. S., 1991, “Determination of the Tolerable Sector of Series Nonlinearities in Uncertain Time-Delay Systems Under Dynamical Output Feedback,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL., Vol. 113, pp. 525–531.
Chen B. S. , and DongT. Y., 1988, “Robust Stability Analysis of Kalman Filter Under Parametric and Noise Uncertainties,” Internat. J. Control, Vol. 48, pp. 2189–2199.
Nahi N. E. , 1978, “Bounding Filter; A Simple Solution to Lack of Exact A Priori Statistics,” IEEE Trans. Information and Control, Vol. 39, pp. 212–224.
Kassam, S. A., Lim, T. L., and Cimini, L. J., 1980, IEEE Trans. on Geoscience and Remote Sensing, Vol. 18, pp. 331–336.
Poor v. , and LoozeD. P., 1981, “Minimax State Estimation for Linear Stochastic Systems with Noise Uncertainty,” IEEE Trans. Automat. Control, Vol. 26, pp. 902–906.
Morris J. M. , “The Kalman Filter: A Robust Estimator for Some Classes of Linear Quadratic Problems,” IEEE Trans. on Information Theory, Vol. 22, pp. 526–534.
Chen, C. T., 1984, Linear System Theory and Design, Saunders College Publishing, Orlando, FL.