Stability analysis of homogeneous finite-time PID control using a small gain theorem ?

摘要

Analysis of adaptive control endowed with homogeneity is a challenging problem due to its nonlinearity, e.g., the homogeneity makes the control indifferentiable, which is a significant obstacle to designing a strict Lyapunov function. Homogeneous finite time PID (FT-PID) control, an extension of classical PID control, is the most straightforward adaptive control with homogeneity. However, its stability analysis has not yet been provided, even if a target system is a simple double integrator. In this paper we tried providing stability analysis of the FT-PID control using a small-gain theorem for input to state stable (ISS) systems.