Internal Model Controller Design of Linearized Ginzburg-Landau Equation

In this work, an output regulator design in a discrete-time setting is considered for a linearized Ginzburg-Landau equation (GLE) with point observation using the internal model principle. To address model instability, spectrum analysis is presented and utilized for the continuous-time GLE system. In addition, the Cayley-Tustin transform is used for model time discretization and no spatial approximation or model reduction is induced in the time discretization. As for the servo control design, the discrete-time Sylvester regulation equations are constructed and applied. By a state-feedback regulator, the output tracking and disturbance rejection are realized simultaneously for the Ginzburg-Landau equation, which is verified by a set of simulation studies.