Estimation of LISS properties via a quadratic form LISS-Lyapunov function

Compared with input-to-state (ISS) stability in global version, the concept of locally input-to-state (LISS) stability is more relevant and meaningful in practice. However, the local property raises difficulties in estimating the local region, which is seldom seen in literature. It is the aim of this paper is to investigate local regions of initial states and external inputs for the given system. We first present that a system is LISS if it admits a LISS-Lyapunov function. Then incorporating the result of Damidovich, a theorem by virtue of quadratic form LISS-Lyapunov functions to identify LISS properties is established. An example serves as a demonstration.