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This paper presents a technique to design an observer-based control law that will stabilize a linear model following system. We assume that the model dynamics are completely known and has the same order as the plant. The linear matrix inequality approach is utilized in the design of observer-based controller. The controller developed in this investigation is linear and under certain assumptions this controller forces the plant states to follow the states of a model. The controller also guarantees that every system response is asymptotically stable. An example is provided to demonstrate the efficiency of the proposed method.