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This paper addresses the problems of stability and positive observation for positive two-dimensional (2D) discrete-time systems in Roesser model with multiple delays. A novel proof is provided for the necessary and sufficient conditions of asymptotic stability for the positive 2D systems. Based on the obtained results, necessary and sufficient conditions are proposed for the existence of a 2D positive observer. All the proposed conditions are in terms of linear matrix inequalities. [ABSTRACT FROM AUTHOR]

This paper is concerned with neutral stochastic delay differential equations with Markovian switching (NSDDEs-MS). A kind of ψ − function is introduced and some criteria on the attractor for the product of the ψ − function are obtained. By the new criteria, the almost sure stability with the general decay rate of NSDDEs-MS could be examined, including the exponential stability and the polynomial stability. Finally, an example is provided to illustrate the applications of our results clearly. [ABSTRACT FROM AUTHOR]