Integral control on nonlinear spaces: two extensions**This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The first author’s visit to Ghent University has been supported by a CSC scholarship, initiated by the China Scholarship Council. The authors want to thank prof.R.Sepulchre for suggesting the pendulum example.