Sliding mode controller-observer design for SISO linear systems

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A new method is proposed for the asymptotically stable sliding mode observer design for SISO linear systems including disturbance inputs which may not satisfy the matching conditions. A sliding observer design method is presented such that, in the presence of the unmatched uncertainty, the estimated state nearly approaches the actual state. Certain sufficient conditions should be satisfied for the asymptotic stability of the error system. Otherwise, this method ensures only that the estimated state approximately tends to the actual state. The reaching time to the sliding surface, the sliding dynamics of the system, the stability of the reconstruction error system via the Lyapunov method, sufficient conditions for the existence of the sliding mode and the dependency of estimated state upon the magnitude of the unmatched uncertainty are studied.