Matrixes Satisfying Siljak’s Conjecture

Tian, Guoqiang (1981): Matrixes Satisfying Siljak’s Conjecture. Published in: Science Exploration , Vol. 2, No. 1 (March 1982): pp. 69-76.

Abstract

Siljak’s Conjecture on the existence of a symmetric positive definite matrix V having a specified structure and satisfying Liapunov’s matrix equation A*V+VA= -W is shown to be true in cases when A is an orthogonal matrix; when A is a symmetric matrix; when A is a normal matrix or A is the linear combination of nonnegative coefficient of all these matrixes.

• Item Type: MPRA Paper
• Language: English
• Keywords: Matrix; Siljak’s Conjecture
• Subjects: C - Mathematical and Quantitative Methods > C0 - General

References

[1]. N. J. Pullman, Matrix Theory and Its Application, (Selected Topics), New York, 1976, pp. 175-8.

[2] L. T. Grujic and D. D. Siljak, Stability of Large-scale system with stable and Unstable subsystem, Proc (1972) JACC, paper 17-3, pp. 550-3.

[3] D. D. Siljak, Stability of Large-scale systems, Proc. 5th, IFAC Congr., C-32 (1972), pp. 1-11.

[4] J. J. Montemayer and et al. IEEE Trans. Automat Contr., Ac-20 (1975), pp. 572-3.

[5] B. N. Datta, IEEE Trans, Automat, Contr., Ac-22 (1977), pp. 132-3.

[6] Joel N. Franklin, Matrix Theory, Prentice-Hall Inc., Englewood Cliffs, (1978), p. 105.