Abstract
To estimate the states and the uncertainties for multi-input–multi-output (MIMO) systems is significant in control engineering. The paper investigates the estimating performance of a widely-used linear augmented observer (LAO) by quantitatively analyzing the biased term of estimation error, which generalizes the previous studies. Then the necessary and sufficient condition for unbiased estimation of LAO is thoroughly discussed. More importantly, by investigating the observability of MIMO uncertain systems, the paper proves that the estimation of LAO is unbiased if and only if the states and the uncertainties of MIMO uncertain systems are observable. The presented theoretical analysis can help practitioners evaluate the feasibility of estimating the specific uncertainties via LAO in practical systems. Finally, even if the estimation of LAO is biased, the design procedure of extended state observer is presented, which offers the unbiased estimation of total disturbance and the derivatives of output.
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