Stabilizing Control Design by Integrable Differential Passive Outputs*

Differential passivity of a nonlinear system has been introduced as passivity of its variational system. Applying standard passivity-based control techniques to differentially passive systems leads to controllers for the corresponding variational systems. However, it is challenging to construct controllers for the original nonlinear systems if the differential passive outputs are non-exact differential one-forms. In this letter, our objective is to provide a systematic procedure to address this issue when differential passive outputs are integrable, i.e., when non-exact differential passive outputs can be made exact by multiplying them by suitable integrating factors. In particular, under suitable detectability assumptions, we propose one static and two dynamic state feedback stabilizing controllers, where each dynamic controller has a form of input-and output-shaping, respectively. We illustrate their effectiveness by stabilization of counter-current heat exchangers.