Robust Positive Real Synthesis for 2D Continuous Systems via State and Output Feedback

This paper considers the problem of positive real control for uncertain twodimensional (2D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm bounded in both state and measurement output equations. The purpose is the design of controllers such that the resulting closed-loop system is asymptotically stable and strictly positive real for all admissible uncertainties. A version of the positive realness of 2D continuous systems is established. Then, sufficient conditions for the solvability of the positive real control problem via state feedback and dynamic output feedback controllers, respectively, are proposed. A linear matrix inequality approach is developed to construct the desired controllers. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the proposed method.