Stabilization of nonlinear 2D Fornasini-Marchesini and Roesser systems

The paper considers nonlinear 2D systems described by Fornasini-Marchesini and Roesser state-space models. Sufficient conditions for the property of exponential stability are developed in terms of vector Lyapunov functions and a converse stability theorem is proved. A form of passivity, termed exponential passivity, is defined and used, together with a vector storage function, to develop a new control law design algorithm to guarantee exponential stability of the controlled system. As one application, the algorithm is applied to the physically relevant case of systems with nonlinear actuator dynamics.