Robust real‐time parameter estimation for linear systems affected by external noises and uncertainties

Summary A robust adaptive parameter estimation method, based on the application of a full‐order filter capable of rejecting exogenous disturbances, is proposed in this article. A linear matrix inequality condition is proposed to synthesize the desired robust filter, assuming the presence of a known input control with constraints. The filter uses the output of the system to estimate the desired signal that will be employed in the adaptive estimation procedure and, to assure robustness to exogenous noise and unstructured uncertainties, the ℋ∞ guaranteed cost is minimized in the synthesis condition. The filtered signals are then applied to an adaptive procedure to estimate the unknown system's internal parameters, which is also proposed in this article. It is shown that lower values for the ℋ∞ guaranteed cost from the disturbance input to the error output of the filter imply more accurate estimations of the parameters. The efficiency of the proposed estimation technique is illustrated through a simulated model and a physical system has been considered to validate real‐time estimation.