Discounted H₈ Tracking Control for Two-Time-Scale Systems With Application to Permanent Magnet Synchronous Motors

article investigates H8 tracking control problem with a discount factor for two-time-scale systems subject to disturbances. The H8 controller design is reduced to solving a set of linear matrix inequalities by using Lyapunov functions with two-time-scale structure. Under the obtained controller, the closed-loop system can track the output of a nonasymptotically stable reference model and achieve the H8 performance for the given attenuation level and discount factor. The stability of the closed-loop system under the developed controller is proven. Com-pared with the existing discounted tracking control meth-ods, the proposed method is capable of avoiding the complicated process of calculating the upper bound of the discount factor to guarantee the stability of the closed-loop system. The effectiveness of our theoretical results is demonstrated through both simulation and experiment on speed control of permanent magnet synchronous motor.