Abstract
In this paper, we study the stability analysis of discrete-time interconnected positive systems by means of a weighted <i>l</i><sub>1</sub>-induced norm, where the weighted <i>l</i><sub>1</sub>-induced norm is computed from the <i>l</i><sub>1 </sub>norm of the input and output signals evaluated with given weighting vectors. In the literature,it was shown that the weighted <i>L</i><sub>1</sub>-induced norm of continuous-time LTI positive systems can be characterized by linear programming problem (LP). Moreover, the weighted <i>L</i><sub>1</sub>-induced norm was proved to be useful for the stability analysis of interconnected positive systems. On the basis of these results, we first show that the weighted <i>l</i><sub>1</sub>-induced norm of discrete-time LTI positive systems can be again characterized by LP. From this preliminary result, we can construct a transformation from a given discrete-time positive system to a continuous-time positive system, where the weighted <i>L</i><sub>1</sub>-induced norm of the resulting system is equivalent to the weighted <i>l</i><sub>1</sub>-induced norm of the original system. By means of this key transformation, we can readily extend the continuous-time case results to the stability analysis of discrete-time interconnected positive systems.
| Original language | Japanese |
|---|---|
| Pages (from-to) | 355-364 |
| Number of pages | 10 |
| Journal | システム制御情報学会論文誌 |
| Volume | 26 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2013 |