Local State-Independent Input-to-Output Stability as a Tool for Robustness Analysis of Mechanical Systems

State-independent input-to-output stability (SIIOS) is known as an extension of input-to-state stability, and it plays a significant role in elucidating an influence from an (external) input to an output on nonlinear systems without considering the value of the state. In this study, we investigate a local version of SIIOS; we introduce the concept of local SIIOS (LSIIOS) for nonlinear systems and demonstrate that an unboundedness observable system is characterized by LSIIOS if it admits an LSIIOS Lyapunov function as the main theorem. As an application of the main theorem, we demonstrate an analysis of a robot controller, passivity velocity field control (PVFC), for an n-link manipulator. The analysis indicates that the closed-loop system based on PVFC is characterized by LSIIOS if an output function of the system is designed to meet a control object of the application. As PVFC is a local controller and the value of state x plays no role in meeting a control object, the analysis results obtained using LSIIOS indicate that LSIIOS and the main theorem are useful for analyzing nonlinear systems such as a local controller.