The output power fluctuations of renewable energy power plants such as wind turbine generators and photovoltaic systems result in frequency deviations and terminal voltage fluctuations. Furthermore, these power fluctuations also affect the turbine shaftings of diesel generators and gas-turbine generators which are the main power generation systems on isolated islands. Therefore, it is important to achieve torsional torque suppression. Since the measurement of torsional torque is technically difficult, and there is an uncertainty in the mechanical constants of the shaft torsional system. This paper presents an estimation system that estimates torsional torque by using a developed $H_{infty}$ observer. In addition to the above functions, the proposed shaft torque observer incorporates a parameter identification system that aims to improve the estimation accuracy. The simulation results validate the effectiveness of the proposed $H_{infty}$ observer and the parameter identification.