This paper proposes a systematic approach to design control laws for a turboprop engine. The proposed approach includes interactions decoupling and control laws design based on linear matrix inequality (LMI). First, since the main objective of the turboprop engine control system is to ensure propeller-absorbed power at a constant propeller speed, the linear model of a turboprop engine can be linearized into a two-input two-output (TITO) plants, and there exist the interactions between two control loops. Because inverted decoupling can well retain the dynamic characteristics of the original system, it is used to decouple the interactions so that the TITO plant can be divided into two single-input single-output plants, that is, gas-generator shaft speed is controlled by fuel flowrate and power turbine shaft speed is controlled by blade angle. Then, the control laws are designed separately for each control loop by solving the LMI group derived from static output feedback (SOF) and regional pole placement. Finally, the proposed approach is implemented on a two-spool turboprop engine (TSTPE) integrated model. The simulation results show that there exist strong interactions between two control loops of TSTPE, applying inverted decoupling to decouple these interactions is effective, and the gas-generator shaft speed and the power turbine speed can track their commands with appropriate performance by controlling the fuel flowrate and blade angle under the action of the designed control laws and inverted decoupling.