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In linear systems theory it's a well known fact that a regulator given by thecascade of an oscillatory dynamics, driven by some regulated variables, and ofa stabiliser stabilising the cascade of the plant and of the oscillators hasthe ability of blocking on the steady state of the regulated variables anyharmonics matched with the ones of the oscillators. This is the well-celebratedinternal model principle. In this paper we are interested to follow the samedesign route for a controlled plant that is a nonlinear and periodic systemwith period T : we add a bunch of linear oscillators, embedding n o harmonicsthat are multiple of 2$\pi$/T , driven by a "regulated variable" of thenonlinear system, we look for a stabiliser for the nonlinear cascade of theplant and the oscillators, and we study the asymptotic properties of theresulting closedloop regulated variable. In this framework the contributions ofthe paper are multiple: for specific class of minimum-phase systems we presenta systematic way of designing a stabiliser, which is uniform with respect to no , by using a mix of high-gain and forwarding techniques; we prove that theresulting closed-loop system has a periodic steady state with period T with adomain of attraction not shrinking with n o ; similarly to the linear case, wealso show that the spectrum of the steady state closed-loop regulated variabledoes not contain the n harmonics embedded in the bunch of oscillators and thatthe L 2 norm of the regulated variable is a monotonically decreasing functionof n o. The results are robust, namely the asymptotic properties on theregulated variable hold also in presence of any uncertainties in the controlledplant not destroying closed-loop stability.

Nonlinear Robust Periodic Output Regulation of Minimum Phase Systems