Estimation of LISS (local input-to-state stability) properties for nonlinear systems

Compared with input-to-state stability (ISS) in global version, the concept of local input-to-state stability (LISS) is more relevant and meaningful in practice. The key of assessing LISS properties lies in investigating three main ingredients, the local region of initial states, the local region of external inputs and the asymptotic gain. It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function. Given developments of linear matrix inequality (LMI) methods, this algorithm is effective and powerful. A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.