Digital control of nonlinear systems: optimal linearisation-based digital redesign approach

Abstract

A new digital redesign technique for nonlinear systems based on the new stabilisable optimal linear model of the nonlinear system is proposed. The term digital redesign herein involves the process of converting a pre-designed analogue state-feedback controller into an equivalent digital one, in the state-matching sense. A constructive digital redesign algorithm is formulated in terms of bilinear and linear matrix inequalities. It is shown that the proposed methodology achieves Lagrange stability of the nonlinear system controlled by the digitally redesigned controller. An illustrative example is presented to demonstrate the effectiveness of the proposed method.