# Article

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Keywords:
design problem; parameter uncertainty; linear systems; stabilization; algebraic Riccati equations; $H_\infty$ output feedback control
Summary:
The robust and reliable $H_{\infty }$ output feedback controller design problem is investigated for uncertain linear systems with actuator failures within a prespecified subset of actuators. The uncertainty considered here is time- varying norm-bounded parameter uncertainty in the state matrix. The output of a faulty actuator is assumed to be any arbitrary energy-bounded signal. An observer-based output feedback controller design is presented which stabilizes the plant and guarantees an $H_{\infty }$-norm bound on attenuation of augmented disturbances, for all admissible uncertainties as well as actuator failures. The construction of the observer-based output feedback control law requires the positive-definite solutions of two algebraic Riccati equations. The result can be regarded as an extension of existing results on robust $H_{\infty }$ control and reliable $H_{\infty }$ control of uncertain linear systems.
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