On Strict Homogeneous Lyapunov Function for Generalized Homogeneous PI Controller

Yu Zhou (1) , Andrey Polyakov (1) , Gang Zheng (2)

1 VALSE - Finite-time control and estimation for distributed systems
2 DEFROST - Deformable Robots Simulation Team

This paper investigates a generalized homogeneous PI (Proportional-Integral) control for a linear plant. A Lyapunov function for analysis of the closed-loop system is designed. For negative homogeneity degree, the obtained Lyapunov function becomes a strict Lyapunov function allowing an advanced analysis to be provided. In particular, a class of the disturbances to be rejected by the control law is characterized, a maximum control magnitude and the settling-time of the closedloop system are estimated.

Domaines: Automatique

Yu Zhou, Andrey Polyakov, Gang Zheng. On Strict Homogeneous Lyapunov Function for Generalized Homogeneous PI Controller. The 60th Conference on Decision and Control, Dec 2021, Austin, United States. ⟨hal-03349701⟩