In recent years, the application of solid oxide fuel cells is increasingly progressed as popular sustainable
energy resources. The most advantage of the solid oxide fuel cells is that they can work in high
temperatures to cooperation with other power generators for achieving a high-performance hybrid
plant. In this paper, a hybrid system including the Gas turbine along with solid oxide fuel cells is
utilized to design a reliable power generating system. Designing a proper control system for the
hybrid solid oxide fuel cell and the gas turbine makes a significant impact on the system’s robustness.
The main purpose of this study is to propose a control strategy to improve the system’s lifetime.
The most important part of the present study is to consider the system model uncertainties and to
utilize the interval analysis for solving a model of the considered hybrid system in the presence of
interval uncertainties derived from its parameters. The final result of this method is to achieve a
confidence interval for the problem. To do so, an extended version of the LQG control methodology
based on interval analysis is proposed for obtaining a robust and optimal solution. Chebyshev inclusion
method is utilized for solving the Riccati equation of the LQG system. Simulation results show a higher
efficiency of the proposed system and its impact on the reliability of the system by performing a
comparison with the ordinary LQR controller and De-centralized method for showing the efficiency of
the proposed method.