LMI Design Procedure for Incremental Input/Output-to-State Stability in Nonlinear Systems

This letter deals with the investigation of an important property that characterizes the detectability of nonlinear systems, namely the incremental Exponential Input/Output-to-State Stability (i-EIOSS). While such a property is easy to check for linear systems, for nonlinear systems it is a hard task. On the other hand, the i-EIOSS property is well-suited for the development of robust estimators. In this letter, we propose a novel numerical design procedure ensuring the computation of the i-EIOSS-related coefficients which are necessary to tune the parameters of the robust estimators. We first introduce a general simple but useful Lyapunov-based method, then we develop a new Linear Matrix Inequality (LMI) condition guaranteeing the computation of the i-EIOSS coefficients. The proposed design method is easily tractable by numerical software and may be used for several real-world applications. Compared to the existing literature, the proposed method is simpler, provides a finite number of LMIs to be solved, and does not need to convert the system into a new one with linear outputs leading to LMI conditions.