This paper designs, implements, and compares the performance of a H ₂, H _∞, H ₂/ H _∞, and μ ‐ synthesis approach for a V 94.2 gas turbine mounted in Damavand combined cycle power plant. The controllers are designed to maintain the speed and exhaust temperature within their desired intervals and to ensure the robust performance of the gas turbine power plant (GTPP) in the presence of uncertainties and load demand variations. A linear model of the GTPP is first estimated using V94.2 gas turbine real‐time data and an autoregressive with exogenous input (ARX) identification approach, and then verified by residual analysis tests and steady‐state performance. The H ₂, H _∞, H ₂/ H _∞, and μ ‐ synthesis controllers are then designed and implemented to the ARX model of the GTPP. The performance of the approaches is assessed and compared in terms of tracking capability, robustness, and transient performance. Additionally, the controllers' performance is compared to that of a conventional PID approach. Despite the slight variations in the performance, all the controllers exhibited robust stability and good overall performance in the presence of model uncertainties and load variations.