Stability of positive linear discrete-time systems

The main focus of the paper is on the asymptotic behaviour of linear discrete-time positive systems. Emphasis is on highlighting the relationship between asymptotic stability and the structure of the system, and to expose the relationship between null-controllability and asymptotic stability. Results are presented for both time-invariant and time-variant systems.

[1]  A note on upper bounds on the maximum modulus of subdominant eigenvalues of nonnegative matrices , 1988 .

[2]  Iterative methods for approximating the subdominant modulus of an eigenvalue of a nonnegative matrix , 1987 .

[3]  Louis Caccetta,et al.  Positive linear dynamic model of mobile source air pollution and problems of control , 2003 .

[4]  V. Rumchev,et al.  Reachability and controllability of compartmental systems. , 2000 .

[5]  W. Burridge,et al.  “Excitability” , 1933 .

[6]  D. James,et al.  Controllability of positive linear discrete-time systems , 1989 .

[7]  Jon Rigelsford,et al.  Positive 1D and 2D Systems , 2002 .

[8]  V. Rumchev,et al.  A fractional-flow model of serial manufacturing systems with rework and its reachability and controllability properties , 2001 .

[9]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[10]  S. Rinaldi,et al.  Excitability, stability, and sign of equilibria in positive linear systems , 1991 .

[11]  D. James,et al.  The role of non‐negative matrices in discrete‐time mathematical modelling , 1990 .

[12]  Rajendra Bhatia,et al.  Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix , 1990 .

[13]  A. Graham.  Nonnegative matrices and applicable topics in linear algebra , 1987 .

[14]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[15]  H. Wolkowicz,et al.  Bounds for eigenvalues using traces , 1980 .

[16]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.