Fault reconstruction‐based robust tracking control design for periodic piecewise polynomial systems with disturbances.

In this article, we address the topics of fault reconstruction and robust fault‐tolerant tracking control for periodic piecewise polynomial uncertain systems with time‐varying delays, faults and external disturbances. In detail, the periodic piecewise polynomial learning observer system is configured with the intent to concurrently reconstruct the faults and immeasurable states of the system that is being considered. Precisely, the key intent of this study centers around in devising a robust fault‐tolerant tracking control to achieve the tracking performance of the system as intended with mixed H∞$$ {H}_{\infty } $$ and passivity performance. To this end, a robust fault‐tolerant tracking control is designed by incorporating the reconstructed faults and error feedback, which aids in vouching for the outcomes that were desired. Besides, by building the periodic piecewise polynomial Lyapunov–Krasovskii functional and making use of the matrix polynomial lemma and Wirtinger's inequality, certain adequate conditions are procured in the frame of linear matrix inequalities. Subsequently, the required gain values for the devised controller and the configured observer are found by using the established linear matrix inequalities. Ultimately, in order to attest the controller's intrinsic potential and relevance, numerical example along with the simulation results is supplied. [ABSTRACT FROM AUTHOR]