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

抄録

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.