Corrigendum to 'On the control of non-linear processes: an IDA-PBC approach' (H. Ramírez et al., Journal of Process Control 19 (1) (2009) 405¿414)

Abstract

In a recent paper [1], the Interconnection and Damping Assignment Passivity-based Control (IDA-PBC) method [2] is studied in the case when the key matching equation is not satisfied. The paper proposes to fix a desired storage function and to design a scaling matrix, which is obtained solving an algebraic Lyapunov equation, in such a way that the linearized dynamics of the closed-loop system is stable – without the need to solve the matching equation. Unfortunately, the derivations in [1] are incorrect, invalidating the results of the paper, in particular, Proposition 1. To explain the problems encountered in [1], in the present note we first re-derive the closed-loop dynamics of a system controlled using the IDA-PBC method in the case when the matching condition is not satisfied, that is, Eq. (11) in [1]. This computations are carried-out following a route, which is slightly different from the one used in [1], that we believe is more general and straightforward. Then, we indicate the points that invalidate Proposition 1.