Reliability-based Control Problem for Systems with Parametric Stochastic Uncertainty

In this paper, we propose a Reliability-Based Anti-Disturbance Control (RADC) approach based on Linear Matrix Inequalities (LMIs) and Constraint State Functions for systems with disturbances and random parameter uncertainties. Unlike traditional robust control methods, our approach explicitly accounts for parametric random uncertainties in controlled systems, along with input disturbances and measurement noise. LMIs are used to define stability and robust performance conditions with a specified level of reliability. By leveraging mathematical techniques, we transform LMIs containing random uncertain parameters into general LMIs, enabling efficient analysis and design. The impact of parameter uncertainties is quantified using reliability indicators, allowing for flexible controller design tailored to varying reliability requirements in industrial production. Finally, simulation outcomes clearly reveal the reliability and robustness of our proposed methodology.