A new LMI condition for decentralized observer-based control of linear systems with nonlinear interconnections

This paper presents a new decentralized observer-based stabilization scheme for a class of nonlinear interconnected systems. A novel linear matrix inequality (LMI) condition is proposed to ensure the asymptotic stability. This improved LMI is established thanks to the use of the well-known Young inequality in a judicious manner. Beside the use of such an inequality, we introduce some additional degrees of freedom which allow to furtherly relax the LMI. Based on the aforesaid, an application of the proposed approach to the design of controllers that are both robust and resilient is presented. Numerical results are shown to demonstrate the validity of our method.