Abstract—This paper is concerned with the stability problem of four-story buildings. It is one of important issues for building safety. The Lyapnov stability theory is applied to four-story buildings, which are dynamical systems represented by mass-spring-damper model. The main objective is to analyze control effort to stabilize the mass-spring-damper model of four-story buildings by using the Fundamental Equations of Constrained Motion and Lyapunov theory. In the initial stage, mass-spring-damper models are oscillated freely without any conditions. Then, we want to stabilize the models using Lyapunov theory by adding additional control forces to control motions of four-story buildings. This paper shows the effectiveness of an application of Lyapunov stability theory with the Fundamental Equation of Constrained Motion to four-story buildings.
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