Stability Analysis of Discrete-time Interconnected Positive Systems using Weighted <i>l</i><sub>1</sub>-induced Norm

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  • 重み付き<i>l</i><sub>1 </sub>誘導ノルムを用いた離散時間結合非負システムの安定性解析
  • 重み付きl₁誘導ノルムを用いた離散時間結合非負システムの安定性解析
  • オモミズキ l ₁ ユウドウ ノルム オ モチイタ リサン ジカン ケツゴウ ヒフシステム ノ アンテイセイ カイセキ
  • Stability Analysis of Discrete-time Interconnected Positive Systems using Weighted l1-induced Norm

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Abstract

In this paper, we study the stability analysis of discrete-time interconnected positive systems by means of a weighted l1-induced norm, where the weighted l1-induced norm is computed from the l1 norm of the input and output signals evaluated with given weighting vectors. In the literature,it was shown that the weighted L1-induced norm of continuous-time LTI positive systems can be characterized by linear programming problem (LP). Moreover, the weighted L1-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 l1-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 L1-induced norm of the resulting system is equivalent to the weighted l1-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.

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