Controller synthesis for positive 2D systems described by the Roesser model

This paper deals with the stability synthesis for a class of 2D linear systems described by the Roesser model. We provide necessary and sufficient conditions for stability, as well as stabilization for linear positive Roesser systems. This kind of systems have the property that the states take nonnegative values whenever the initial boundaries are non-negative. The synthesis of state-feedback controllers, including the requirement of positivity of the controllers and the extension of the results to uncertain plant are solved in terms of linear programming. A numerical example is included to illustrate the proposed approach.