Inverse-dynamics based state and disturbance observers for linear time-invariant systems

An output-feedback observer is proposed in this paper to simultaneously estimate unknown states and disturbances of linear time invariant systems. The states are estimated using a Luenberger-like observer while the disturbance signals are estimated based on an inverse-dynamics motivated algorithm. The proposed schemes can be applied to a wide variety of disturbances since no disturbance model is required in the estimation. Depending on the input/output rank conditions of the plant, two different designs are proposed. The observer gains are selected based on sufficient conditions for exponentially converging estimation. The design procedure is illustrated step-by-step by using two examples: a hypothetical problem and the ground vehicle lateral speed estimation problem. A standard H.-filter is used as the benchmark to illustrate the performance of the proposed method.