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In this article, we address the disturbance rejection problem for linear plants with delayed measured output. The output delay is allowed to be time‐varying and of arbitrary duration. The disturbances that may represent actuator faults are generated by an exogenous dynamic system and can be matched or unmatched. A predictor–based observer is designed via the PDE–backstepping (Partial Differential Equation–backstepping) method so that an estimate of the current state vector, as well as that of unmeasured disturbance, can be obtained. These estimates are used in to regulate the output and reject the disturbance by output feedback sliding mode control. In addition, a solution for finite‐time disturbance rejection (rather than exponential only) is also introduced when the sensor delay is constant. Numerical examples illustrate the performance and robustness of the both proposed predictor‐feedback control systems. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a new adaptive sliding mode control approach via output feedback for a class of nonlinear systems. The sliding‐mode based controller can deal with parametric uncertainties and (un)matched disturbances with unknown upper bounds. Finite‐time convergence of the tracking error to a predefined neighborhood of the origin of the closed‐loop system is proved with guaranteed transient and steady‐state performance. Basically, the novelty of our result lies on combining two important adaptation tools: monitoring and barrier functions. The adaptation process is divided into two stages, where an appropriate monitoring function allows for the specification of performance criteria during the transient phase, while the barrier function ultimately confines the tracking error within a small residual set in steady state. Simulation results including an application to Anti‐lock Braking System illustrate the advantages of the proposed adaptive control strategy. [ABSTRACT FROM AUTHOR]