Stabilization of LTI systems with both uncertainties and external disturbances via DE-based control method

This paper is concerned with the stabilization of linear time-invariant (LTI) systems with unknown parameters and external disturbances. Firstly, four types of suitable filters are presented and applied to achieve the accuracy estimate of the disturbances. Based on these filters, four types of disturbance estimators are designed and used to asymptotically cancel the corresponding disturbances. Secondly, an adaptive disturbance estimator (DE)-based control method is obtained by combining the adaptive control method with the DE-based control method. It is noted that the algebraic representation of the adaptive feedback control law is given in a more concise form by the tool of the semi-tensor product of matrix. Further, the stabilization of LTI systems is achieved by the obtained adaptive DE-based control method. Finally, three numerical examples with computer simulation are provided to verify the correctness and validity of the obtained theoretical methods.