Uniform sample generations from contractive block Toeplitz matrices

IEEE Transactions on Automatic Control

Volumn 51, Issue 9, 2006, Pages 1559-1565

  Zhou, Tong ^a   Feng, Chao ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Model set validation; Monte Carlo method; Random matrix; Robust control; Toeplitz matrix; Uniform distribution

Indexed keywords

INVARIANCE; MATRIX ALGEBRA; MONTE CARLO METHODS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; ROBUSTNESS (CONTROL SYSTEMS);

MODEL SET VALIDATION; RANDOM MATRIX; TOEPLITZ MATRIX; UNIFORM DISTRIBUTION;

SAMPLED DATA CONTROL SYSTEMS;

EID: 33749038664     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.880810     Document Type: Article

References (18)

1. B. Barmish and C. Lagoa, "The uniform distribution: A rigorous justification for its use in robustness analysis," Math. Control, Signals, Syst., vol. 10, pp. 203-222, 1997.
2. V. Blondel and J. Tsitsiklis, "A survey of computational complexity results in systems and control," Automatica, vol. 36, pp. 1249-1274, 2000.
3. G. Calafiore and F. Dabbene, "A probabilistic framework for problems with real structured uncertainty in systems and control," Automatica, vol. 38, pp. 1265-1276, 2002.
4. G. Calafiore, F. Dabbene, and R. Tempo, "Randomized algorithms for probabilistic robustness with real and complex structured uncertainty," IEEE Trans. Autom. Control, vol. 45, no. 12, pp. 2218-2235, Dec. 2000.
5. ∞ Approach. New York: Wiley, 2000.
6. X. Chen, K. Zhou, and J. Aravene, "Fast construction of robustness degradation function," SIAM J. Control Optim., vol. 42, no. 6, pp. 1960-1971, 2004.
7. K. Fang and Y. Zhang, Generalized Multivariate Analysis. Berlin, Germany: Springer-Verlag, 1990.
8. C. Feng, "Random tranfer function generation and its applications," M.S. thesiis, Tsinghua Univ., Beijing, China, 2006.
9. C. Feng and T. Zhou, Remarks on Monte-Carlo methods in model set validation submitted for publication.
10. J. Gentle, Random Number Generation and Monte Carlo Methods, 2nd ed. New York: Springer-Verlag, 2003.
11. A. Mathai, Jacobians of Matrix Transformations and Functions of Matrix Argument. Singapore: World Scientific, 1997.
12. M. Mehta, Random Matrices, 2nd ed. Boston, MA: Academic, 1991.
13. L. Ray and R. Stengel, "A Monte Carlo approach to the analysis of control system robustness," Automatica, vol. 29, pp. 229-236, 1993.
14. C. Robert and G. Casella, Monte Carlo Statistical Methods. Berlin, Germany: Springer-Verlag, 1999.
15. ∞ with applications to risk-adjusted performance analysis and model (in)validation," IEEE Trans. Autom. Control, vol. 50, no. 3, pp. 410-416, Mar. 2005.
16. R. Tempo, E. Bai, and F. Dabbene, "Probabilistic robustness analysis: Explicit bounds for the minimum number of samples," Syst. Control Lett., vol. 30, pp. 237-242, 1997.
17. T. Zhou and H. Kimura, "Time domain identification for robust control," Syst. Control Lett., vol. 20, pp. 167-178, 1993.
18. T. Zhou, L. Wang, and Z. Sun, "Model set validation under a stochastic framework," Automatica, vol. 38, no. 9, pp. 1449-1461, 2002.