INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2009; 19:1168–1196 Published online 9 September 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/rnc.1378 A homotopy method for exact output tracking of some non-minimum phase nonlinear control systems L. Consolini 1, ∗, † and M. Tosques 2 1 Dipartimento di Ingegneria dell’informazione, Viale Usberti 181/A, 43100 Parma, Italy 2 Dipartimento di Ingegneria Civile, Viale Usberti 181/A, 43100 Parma, Italy SUMMARY This paper presents a method for non-causal exact dynamic inversion for a class of non-minimum phase nonlinear systems, which seems to be an alternative to those existing in the literature. This method is based on a homotopy procedure that allows to find a ‘small’ periodic solution of a desired equation by a continuous deformation of a known periodic solution of a simpler auxiliary system. This method allows to face the exact output tracking problem for some non-minimum phase systems that are well known in the literature, such as the inverted pendulum, the motorcycle and the CTOL aircraft. Copyright 2008 John Wiley & Sons, Ltd. Received 20 April 2007; Revised 19 June 2008; Accepted 23 July 2008 KEY WORDS: nonlinear non-minimum phase systems; output tracking; dynamic inversion 1. INTRODUCTION In this paper we consider the problem of exact output tracking a periodic reference trajectory  for a suitable family of non-minimum phase nonlinear control systems, which includes some well-known benchmarks for nonlinear control theory such as the inverted pendulum [1, 2], the VTOL aircraft [3–6], the motorcycle [7] and the CTOL aircraft [8, 9]. Solving the exact output tracking problem for one of these systems, the resulting unstable internal dynamic has the form ¨  = f (t , ) (1) our goal is to find an initial condition for Equation (1), such that the resulting solution is periodic and sufficiently small. To this end we apply a homotopy method that relies essentially on the following steps. We find a family of differential problems dependent on s ¨  = f (t , s , ) such that f (t , 1, ) = f (t , ) and ¨  = f (t , 0, ) admits a ‘small’ periodic solution ˜ . In Theorem 1, we ∗ Correspondence to: L. Consolini, Dipartimento di Ingegneria dell’Informazione, Viale Usberti 181/A, Parma, Italy. † E-mail: luca.consolini@polirone.mn.it Copyright 2008 John Wiley & Sons, Ltd.