Nonlinear robust periodic output regulation of minimum phase systems

In linear system theory, it is a well-known fact that regulator given by the cascade of an oscillatory dynamics, driven some regulated variables, and stabiliser stabilising plant oscillators has ability blocking on steady state variables any harmonics matched with ones oscillators. This well-celebrated internal model principle. this paper, we are interested to follow same design route for controlled nonlinear periodic period T: add bunch oscillators, embedding $$n_o$$ multiple $$2 \pi /T$$ , “regulated variable” system, look study asymptotic properties resulting closed-loop variable. framework, contributions paper multiple: specific class minimum-phase systems present systematic way designing stabiliser, which uniform respect using mix high-gain forwarding techniques; prove T domain attraction not shrinking ; similarly case, also show spectrum steady-state variable does contain n embedded in $$L_2$$ norm monotonically decreasing function . The results robust, namely hold presence uncertainties destroying stability.