ℓ1-induced norm and controller synthesis for positive 2D systems with multiple delays

This paper addresses the problem of ℓ₁-induced controller design for positive two-dimensional (2D) systems with multiple delays. An analytical method is presented to calculate the exact value of ℓ₁-induced norm for positive 2D delayed systems. Necessary and sufficient conditions for asymptotical stability and ℓ₁-induced performance are first derived for the addressed system. Then, based on the singular value decomposition (SVD) technique, controllers are designed to guarantee the asymptotic stability with a prescribed ℓ₁-gain performance level. Those characterizations are formulated in the form of linear programming (LP). Finally, two examples are provided to show the effectiveness and correctness of the theoretical results.