Output feedback control of rational nonlinear systems: A new approach based on passivity indices

Recently, a new strategy for local analysis of passivity indices and its application for output feedback asymptotic stabilization of nonlinear systems was proposed [2]. Polynomial input-affine systems were considered and sum of squares (SOS) techniques were employed for estimating a domain in which the passivity indices are valid and stability is guaranteed. Though simple and useful, the method still demands improvements, as the estimates obtained can be quite conservative. In this context, this work applies the Finsler's Lemma and the notion of linear annihilators for enlarging the estimates of the aforementioned regions of attraction by reformulating the estimation problem as a polytopic LMI condition. In addition, we extended the results of [2] for the class of the rational nonlinear systems with possibly rational Lyapunov functions. Numerical examples are also provided in order to demonstrate the applicability of the method.