Dissipative-based dynamic state feedback design using a geometric decomposition

This paper presents a constructive approach to dynamic state feedback controller design for control affine systems such that the closed-loop system exhibits some desired dissipative properties. The proposed approach relies on the construction of a storage function for a given control affine system together with a dynamic controller structure. Using this approach, it is then possible to shape the Hessian of a potential function associated to the system in the extended space. A damping feedback controller with an injection term is used to ensure desired dissipative properties of the closed-loop system. An example, studied previously in the context of dynamic power-shaping passivity-based control and stabilization, is presented to illustrate the design methodology.