Reliability-based anti-disturbance control for systems with parametric stochastic uncertainty: A probabilistic LMI approach

We propose a reliability-based anti-disturbance control (RADC) method for systems with parametric stochastic uncertainty based on the linear matrix inequality (LMI) and the limit state function. Differing from the existing anti-disturbance control, the parametric stochastic uncertainty is considered in both the concerned system and the exogenous disturbance system. With this consideration, the condition for system stability and performance robustness is described by a stochastic LMI which holds with a certain probability (reliability). Through the limit state function method, the stochastic LMI is subtly transformed into two probabilistic LMIs for two different cases. The proposed probabilistic LMIs contain two probabilistic parameters of reliability indexes that quantify the effect of parametric stochastic uncertainty. At different prescribed reliability indexes, controllers with different reliability can be flexibly and reliably designed. Two illustrative examples with Monte-Carlo verification are presented to demonstrate the feasibility and effectiveness of the proposed RADC method.