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Observer-based sliding mode control of combustion instability in a Rijke-type thermoacoustic system is considered. A commonly used thermoacoustic model with sensors and monopole-like actuators is linearized and formulated in a state-space form. It is assumed that the velocity or pressure sensor locations are chosen to assure the observability of the system. An observer-based sliding mode controller is then implemented to tune the actuators so that the system is asymptotically stable. The effectiveness of the controller is illustrated through a simulation example involving two modes and one sensor. The successful demonstration indicates that the observer-based feedback controller can be applied to a real combustion system with multiple modes. [ABSTRACT FROM AUTHOR]