A robust decentralized observer-based stabilization method for interconnected nonlinear systems: improved LMI conditions

This chapter presents a new decentralized observer-based controller design method for nonlinear discrete-time interconnected systems with nonlinear interconnections. Thanks to some algebraic transformations and the use of a new variant of Young’s inequality, an linear matrix inequality (LMI)-based approach is provided to compute the observer-based controller gain matrices. Furthermore, the congruence principle is used under a judicious and new manner to include additional slack variables and to cancel some bilinear matrix coupling. The resulting final LMI conditions are less conservative compared with the techniques existing in the literature. The effectiveness of the proposed methodology is shown through two illustrative examples.