Lyapunov stability analysis of a robust model reference adaptive PI controller for systems with matched and unmatched dynamics

Abstract

In this paper, the discrete-time Lyapunov stability analysis of a Robust Model Reference Adaptive PI (Proportional-Integral) Controller is presented. The mathematical development of this controller is grounded on Robust Model Reference Adaptive Control philosophy, which provided boundedness of all closed-loop system signals and ensures its global stability. The resulting controller shows robustness characteristics to matched and unmatched dynamics, it guarantees the convergence of adaptive gains to a solution set and the convergence of tracking error to a residual set on steady state. Besides, to implement it, the only required information about the plant are its relative degree and the signal of its gain. Simulation results of the controller are provided, applying it on an unstable nonminimum-phase plant and in a practical plant. Besides, it was also compared with a Robust Model Reference Adaptive Controller and presented higher performance.