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In the paper, a novel methodology of actuator fault estimation for linear discrete-time systems is proposed. To solve such a challenging problem, a quadratic boundedness approach is used to guarantee the convergence of the proposed state and actuator fault estimation method. In the proposed methodology, the robustness is achieved through the unknown input decoupling while an unappealing effect of the undecoupled disturbances is minimized. Moreover, the developed approach enables to obtain a feasible set of joint system state and fault estimation error. Based on this knowledge, a novel methodology of calculating the uncertainty intervals of the system state and actuator fault is proposed. The illustrative part of the paper presents results obtained for the laboratory DC servo-motor and compares the proposed approach with two alternative methods. Based on this real-data example, the efficiency of the …