This paper analyzes the dynamics of a cantilever plate with piezoelectric actuators. A deadbeat state observer is achieved implicitly through processing of the general input-output data and the actual system Markov parameters are recovered from the observer Markov parameters. Finally, the Eigensystem Realization Algorithm (ERA) is then employed to develop an explicit state space model of the equivalent linear system. The mathematical model obtained by ERA is controllable and observable and is suitable for the purpose of controller design.