Stabilization of the positive switched 2D linear systems described by the Roesser models

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. Positive linear systems are defined on cones and not on linear spaces. Therefore, the theory of positive systems is more complicated and less advanced. The positive switched 2D linear systems described by the Roesser models are addressed. Necessary and sufficient conditions for the asymptotic stability of the positive switched 2D linear systems described by the Roesser models for any switching are established. The problem of finding a gain matrix of the state-feedback of positive switched 2D linear systems described by the Roesser models such the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. It is shown that stabilization of the positive switched 2D linear systems described by the Roesser models can be reduced to stabilization of the positive switched 1D linear systems.