On Exponential Convergence of Self-Learning Observers for Fault Reconstruction via Halanay's Inequality Approach

Abstract

This work studies the fundamental properties of self-learning observers (LOs), which simultaneously estimate states and parameters resource-efficiently. LOs have a simple structure, the capacity to estimate system uncertainties using only one algebraic equation, and decent performance. We explore the exponential convergence property of LOs in-depth and present an explicit exponential convergence rate for the first time using Halanay's inequality technique. This work further contributes by providing fewer conservative conditions, thereby decreasing the equality condition that must be satisfied in previous studies on LOs. The LO parameters are acquired by solving linear matrix inequalities (LMIs), and the rules for parameter tuning under the new constraints are provided.