INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust. Nonlinear Control 0000; 00:2–24 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/rnc A mixed numerical-analytical stable pseudoinversion method aimed at attaining an almost exact tracking L. Jetto 1 ∗ , V. Orsini 1 , R. Romagnoli 1 1 Dipartimento di Ingegneria dell’Informazione, Universit` a Politecnica delle Marche, Ancona, Italy. SUMMARY This paper considers the problem of computing the input u(t) of an internally asymptotically stable, possibly non minimum phase, linear, continuous-time system Σ yielding a very accurate tracking of a pre-specified desired output trajectory ˜ y(t). The main purpose of the new approach proposed here is to alleviate some limitations inherent the classical methods developed in the framework of the preview based stable inversion, which represents an important reference context for this class of control problems. In particular the new method allows one to deal with arbitrary and possibly uncertain initial conditions and does not require a pre-actuation. The desired output ˜ ys(t) to be exactly tracked in steady-state is here assumed to belong to the set of polynomials, exponential and sinusoidal time functions. The desired transient response ˜ y t (t) is specified to obtain a fast and smooth transition towards the steady-state trajectory ˜ ys(t), without under and/or overshoot in the case of a set point reset. The transient control input u t (t) is ”a priori” assumed to be given by a piecewise polynomial function. Once ˜ y(t) has been specified, this allows the computation of the unknown u t (t) as the approximate least-squares solution of the Fredholm’s integral equation corresponding to the explicit formula of the output forced response. The steady-state input us(t) is analytically computed exploiting the steady-state output response expressions for inputs belonging to the same set of ˜ y s (t). Copyright c ⃝ 0000 John Wiley & Sons, Ltd. Received . . . KEY WORDS: Feed-forward control, almost perfect output tracking, model stable pseudo-inversion Copyright c ⃝ 0000 John Wiley & Sons, Ltd. Prepared using rncauth.cls [Version: 2010/03/27 v2.00]