PID Controller Design for Multivariable Systems Using Gershgorin Bands

A method to design decentralized PID controllers for MIMO systems is presented in this paper. Each loop is designed separately, but the Gershgorin bands are considered to take interactions into account. The method uses different design parameters: The infinity norm of the complementary sensitivity function as well as the crossover frequency are considered to represent the closed-loop system performances. A third design parameter, defined as the minimal distance from the critical point to the Gershgorin band is used to provide the desired stability robustness to the MIMO closed-loop system.