A survey on semi-tensor product of matrices

Journal of Systems Science and Complexity

Volumn 20, Issue 2, 2007, Pages 304-322

  Cheng, Daizhan ^a   Qi, Hongsheng ^a   Xue, Ancheng ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

Abstract algebra; Differential geometry; Dynamic systems; Logic; Semi tensor product

Indexed keywords

ABSTRACT ALGEBRA; DIFFERENTIAL GEOMETRY; SEMI TENSOR PRODUCTS;

DYNAMICAL SYSTEMS; FORMAL LOGIC; GEOMETRY; TENSORS;

MATRIX ALGEBRA;

EID: 34249105607     PISSN: 10096124     EISSN: 15597067     Source Type: Journal    
DOI: 10.1007/s11424-007-9027-0     Document Type: Conference Paper

References (43)

1. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Vol. 1), Cambridge Press, Cambridge, 1991.
2. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Vol. 2), Cambridge Press, Cambridge, 1991.
3. D. Cheng, Matrix and Polynomial Approach to Dynamic Control Systems, Science Press, Beijing, 2002.
4. D. Cheng and H. Qi, Semi-tensor Product of Matrices - Theory and Applications, Science Press, Beijing, 2007.
5. J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Ed.), John Wiley &: Sons, Chichester, 1999.
6. W. M. Boothby, An Introduction to Differential Manifolds and Riemannian Geometry (2nd Ed.), Academic Press Inc., Oriando, 1986.
7. L. Zhang, D. Cheng, and C. Li, The general structure of cubic matrices (in Chinese), Sys. Sci. Math. Sci., 2005, 25(8): 439-450.
8. J. G. Zaborszky, J. G. Huang, B. Zheng, and T. C. Leung, On the phase protraits of a class of large nonlinear dynamic systems such as the power systems, IEEE Trans. Autom. Contr., 1998, 33(1): 4-15.
9. H. D. Chiang, M. Hirsch, and F. Wu, Stability regions of nonlinear autonomous dynamical systems, IEEE Trans. Automat. Contr., 1988, 33 (1): 16-27.
10. D. Cheng and J. Ma, Calculation of stability region, in Proc. 42nd IEEE Conference on Decision and Contrat 2003, Maui, 2003, 5615-5620.
11. D. Cheng, J. Ma, Q. Lu, and S. Mei, Quadratic form of stable sub-manifold for power systems, Int. J. Robust and Nonlinear Control, 2004, 14(9-10): 773-788.
12. D. Cheng, Semi-tensor product of matrices and its applications to dynamic systems, in New Directions and Applications in Control Theory (ed. by W. Dayawansa, A. Lindquist, and Y. Zhou), Lecture Notes in Control and Information Sciences, Springer, Netherlands, 2005, 61-79.
13. J. Ma, D. Cheng, Y. Hong, and Y. Sun, On complexity of power systems, J. Sys. Sci. & Complexity, 2003, 16(3): 391-403.
14. J. Ma, D. Cheng, S. Mei, and Q. Lu, Approximation of the boundary of power system stability region based on semi-tensor theory, Part One: theoretical basis (in Chinese), Auto. Elec. Power Sys., 2006, 30(10): 1-5.
15. J. Ma, D. Cheng, S. Mei, and Q. Lu, Approximation of the boundary of power system stability region based on semi-tensor theory, Part Two: application (in Chinese), Auto. Elec. Power Sys., 2006, 30(11): 1-6.
16. F. Zhang, Matrix Theory, Basic Results and Techniques, Springer-Verlag, New York, 1999.
17. D. Cheng, X. Hu, and Y. Wang, Non-regular feedback linearization of nonlinear systems via a normal form algorithm, Automation, 2004, 40(3): 439-447.
18. J. Zhong, M. Karasalo, D. Cheng, and X. Hu, New results on non-regular linearization of nonlinear systems, Int. J. Contr., accepted.
19. D. Cheng, G. Yang, and Z. Xi, Nonlinear systems possessing linear symmetry, Int. J. Robust Nonli. Contr., to appear.
20. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, 1972.
21. D. Cheng, Some applications of semi-tensor product of matrix in algebra, Comp. Math with Appl., to appear.
22. R. A. Abraham, J. E. Marsden, Foundations of Mechanics (2nd Ed.), Benjamin/Cummings Pub. Com. Inc., London, 1978.
23. D. Cheng, On logic-based intelligent systems, in Proc. International Conference on Control and Automation 2005, Budapest, 2005, 71-76.
24. D. Cheng and H. Qi, Matrix expression of logic and fuzzy control, in Proc. 44th IEEE Conference on Decision and Control, Seville, 2005, 3273-3278.
25. L. Rade and B. Westergren, Mathematics Handbook for Science and Engineering (4th Ed.), Studentlitteratur, Sweden, 1998.
26. A. C. Xue, Felix F. Wu, Y. Ni, Q. Lu, and S.W. Mei, Power system transient stability assessment based on quadratic approximation of stability region, Electric Power Systems Research, 2006, 76: 709-715.
27. A. C. Xue, C. Shen, S. Mei, Y. Ni, F. F. Wu, and Q. Lu, A new transient stability index of power systems based on theory of stability region and its applications, in Proceedings of 2006 IEEE PES General Meeting, Montreal, Quebec, Canada, June 18-22, 2006.
28. R. J. Kaye and F. F. Wu, Dynamic security regions of power systems, IEEE Transactions on Circuits & Systems, 1982, 29(9): 612-623.
29. Y. Yu, Security region of bulk power system, in Proceeding of the 2002 International Conference on Power System Technology, Kunming, China, 2002, 13-17.
30. A. C. Xue, F. F. Wu, Q. Lu, and S. W. Mei, Power system dynamic security region and its approximation, IEEE Transactions on Circuits and Systems I: Regular Papers, 2006, 53: 2849-2859.
31. A. C. Xue, S. W. Mei, Q. Lu, and F. F. Wu, Approximation for the dynamic security region of network-reduction power systems (in Chinese), Automation of Electric Power Systems, 2005, 29: 18-23.
32. A. C. Xue, W. Hu, S. Mei, Y. Ni, F. F. Wu, and Q. Lu, Comparison of linear approximations for the dynamic security region of network-reduction power system, in Proceedings of 2006 IEEE PES General Meeting, Montreal, Quebec, Canada, June 18-22, 2006.
33. H. D. Chiang, F. F. Wu, and P. P. Varaiya, Foundation of direct methods for power systems transient stability analysis, IEEE Transactions on Circuits and Systems, 1987, 34: 160-173.
34. D. Cheng and Y. Dong, Semi-tensor product of matrices and its some applications to physics, Methods and Applications of Analysis, 2003, 10(4): 565-588.
35. D. Cheng, Semi-tensor product of matrices and its application to Morgan's problem, Science in China (Series F), 2001, 44(3): 195-212.
36. D. Cheng, On semi-tensor product of matrices, Abs. International Conference of Chinese Mathematicians 2001, Taipei, 33, 2001.
37. D. Cheng, A new matrix product and its applications, in Abs., Int. Congress of Mathematicians, Beijing, 2002, 367.
38. D. Cheng and L. Zhang, Generalized normal form and stabilization of nonlinear systems, Int. J. Control, 2003, 76(2): 116-128.
39. D. Cheng and L. Zhang, On semi-tensor product of matrices and its applications, ACTA Math. App. Sinica, 2003, 18(4): 219-228.
40. H. D. Chiang and F. F. Wu, Foundations of the potential energy boundary surface method for power system transient stability analysis, IEEE Trans. Circ. Sys., 1988, 35(6): 712-728.
41. K. Truemper, Design of Logic-Based Intelligent Systems, Wiley & Sons, New Jersey, 2004.
42. A. C. Xue, K. L. Teo, Q. Lu, and S. W. Mei, Polynomial approximations for the stable and unstable manifolds of the hyperbolic equilibrium point using semi-tensor product, International Journal of Innovative Computing, Information and Control, 2006, 2: 593-608.
43. G. Yang and D. Cheng, Structure of m-th order nonlinear systems possessing rotation symmetry (in Chinese), J. Sys. Sci. &: Math. Sci., 2004, 24(1): 138-144.