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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.

This paper deals with the controller synthesis for a class of positive two-dimensional (2D) switched delay systems described by the Roesser model. This kind of systems has the property that the states take nonnegative values whenever the initial boundaries are nonnegative, some delay-dependent sufficient conditions for the exponential stability of positive 2D switched systems with state delays are given. Furthermore, the design of positive state feedback controller under which the resulting closed-loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities (LMIs). An example is included to illustrate the effectiveness of the proposed approach. © 2014 Elsevier Inc. All rights reserved