Multivariable PID controller synthesis of discrete linear systems based on LMIs

We investigate a new approach for multivariable PID controller synthesis for time-discrete linear systems. The design of multivariable PID controller is challenging because it is necessary to consider coupling effects. As yet, there is no simple general method to solve this problem. This paper should contribute to find a solution. For the presented method a extended state space representation of the time-discrete closed-loop is necessary. The Schur complement is used to reformulate the Lyapunov stability theorem. This yields a non-linear matrix inequality. The non-linear component in this Schur complement is linearized by the Neumann series. Thus, we have a linear matrix inequality (LMI). This LMI is used to build an iterative algorithm, which determines the PID control parameters. We evaluate this algorithm on two examples to illustrate the results.