Control with Positivity Constraint for 2D Continuous-Time Systems in Roesser Model

This paper deals with the stability synthesis for a class of 2D continuous-time systems described by the Roesser model. Conditions for stability and stabilization of positive continuous-time Roesser systems are derived, for which the states take non-negative values whenever the initial conditions are non-negative. As well, the synthesis of state-feedback controllers, including the requirement of positiveness of the controllers, and its extension to uncertain plants are solved in terms of linear programming. In addition, the synthesis problem with non-symmetrical bounds and stabilization are also treated. Numerical examples are included to illustrate the proposed approach.