Stabilization of Linear Time-Invariant Systems With Unbounded Disturbances via DE-Based Control Method

This paper investigates the stabilization problem of linear time-invariant (LTI) systems with unbounded disturbances. Firstly, three suitable filters are designed to asymptotically estimate the corresponding external disturbances:
${w}(t)= {p}\cos (3t) + q$
,
$w(t)=pe^{0.1t}$
, and
$(p\cos (3t)+q){e^{0.1t}}$
, where
$p, q$
are unknown constants. Secondly, a disturbance estimator (DE)-based control strategy is proposed by combining the linear feedback control method with the obtained filters, and thus the stabilization of such systems is realized. It is the first time to suppress the unbounded disturbances by designing suitable filters. Thus, the presented conclusions have some advantages over the existing ones. Finally, illustrative examples with computer simulation verify the effectiveness and correctness of the proposed results.