Necessary and sufficient stability criterion and stabilization for positive 2‐D continuous‐time systems with multiple delays

This paper addresses the stability and control problem of the linear positive two-dimensional (2-D) continuous-time systems in Roesser model with multiple time delays. The contribution lies in two aspects. First, a simple novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for 2-D continuous delayed systems. It turns out that the magnitude of delays has no any impact on the stability of these systems, which is completely determined by the system matrices. Second, a necessary and sufficient condition for the existence of state-feedback controllers is proposed for general delayed 2-D systems, which ensures the non-negativity and the stability of the resulting closed-loop systems. Two examples are given to validate the proposed methods.