Stability of positive continuous-time linear systems with delays

The asymptotic stability of positive continuous-time linear systems with delays is addressed. It is shown that: 1) the asymptotic stability of the positive systems with delays is independent of their delays, 2) the checking of the asymptotic stability of the positive systems with delays can be reduced to checking of the asymptotic stability of positive systems without delays. Simple stability conditions for the positive systems with delays are give and illustrated by numerical examples.

[1]  Bui The Anh,et al.  Stability radii of positive higher order difference systems under fractional perturbations , 2010 .

[2]  M. Twardy,et al.  On the alternative stability criteria for positive systems , 2007 .

[3]  Tadeusz Kaczorek,et al.  The Choice of the Forms of Lyapunov Functions for a Positive 2D Roesser Model , 2007, Int. J. Appl. Math. Comput. Sci..

[4]  T. Kaczorek.  Positive 1D and 2D Systems , 2001 .

[5]  M. Busłowicz.  Robust stability of positive discrete-time linear systems with multiple delays with linear unity rank uncertainty structure or non-negative perturbation matrices , 2007 .

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

[7]  Abdellah Benzaouia,et al.  Positive stabilization of discrete-time systems with unknown delay and bounded controls , 2007, 2007 European Control Conference (ECC).

[8]  Tadeusz Kaczorek,et al.  Practical stability of positive fractional discrete-time linear systems , 2008 .

[9]  Tadeusz Kaczorek,et al.  Robust stability of positive discrete-time interval systems with time-delays , 2004 .

[10]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[11]  Springer. Niculescu,et al.  Delay effects on stability , 2001 .

[12]  Henryk Górecki,et al.  Analysis and Synthesis of Time Delay Systems , 1989 .

[13]  M. Buslowicz.  Simple stability conditions for linear positive discrete-time systems with delays , 2008 .

[14]  Nguyen Khoa Son,et al.  Stability radii of higher order positive di erence systems , 2003 .