Necessary and sufficient conditions for robust stability of the positive discrete-time interval system with time-delays are established.
It is shown that this system is robustly stable if and only if one well de?ned positive discrete-time system with time-delays is asymptotically stable. The considerations are illustrated by numerical example.
Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed conditions are compared with the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.
Simple new necessary and sufficient conditions for asymptotic stability of the positive linear discrete-time systems with delays in states are established. It is shown that asymptotic stability of the system is equivalent to asymptotic stability of the corresponding positive discrete-time system without delays of the same size. The considerations are illustrated by numerical examples.