#### Glasnik Matematicki, Vol. 40, No.1 (2005), 121-132.

### GLOBAL DEPENDENT STABILITY CRITERION FOR TIME
DISCRETE LINEAR SYSTEMS

### X. H. Tang and S. S. Cheng

Department of Applied Mathematics,
Central South University, Changsha, Hunan 410083, P.R. China

*e-mail:* `tangxh@mail.csu.edu.cn`
Department of Mathematics, Tsing Hua University,
Hsinchu 30043, Taiwan, ROC

**Abstract.** It is shown that every solution of the linear
difference system with constant coefficients and delays tends to zero
if a certain matrix derived from the coefficient matrix is a M-matrix
and the diagonal delays satisfy delay dependent conditions.

**2000 Mathematics Subject Classification.**
39A10, 39A11.

**Key words and phrases.** M-matrix, delay, stability.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.40.1.11

**References:**

- H. Matsunaga and T. Hara,
*The asymptotic stability of a two-dimensional linear delay difference equation*,
Dynamics of Cont. Discrete Impulsive Sys. **6** (1999), 465-473.

- J. W. Wu and K. S. Hong,
*Delay-independent exponential stability criteria for time varying discrete delay systems*,
IEEE Trans. Automatic Control **39** (1994), 811-814.

CrossRef

- M. Fiedler,
Special Matrices and Their Applications in Numerical Mathematics,
Martinus Nijhoff Publ. (Kluwer), Dordrecht, 1986.

- B. Bapat and T. E. S. Raghavan,
Nonnegative Matrices and Applications, Cambridge University Press, Cambridge, 1997.

*Glasnik Matematicki* Home Page