Robust controller design for multivariable systems under nonstationary parametric variations and bounded external disturbances

This paper considers linear multivariable systems with physical parameters varying from their known nominal values in an arbitrary and nonstationary manner. The plant is subjected to polyharmonic external disturbances containing an arbitrary number of unknown frequencies with unknown amplitudes having a bounded sum. The problem is to design a controller that robustly stabilizes the closed loop system and ensures desired errors for the controlled variables of the plant with nominal parameters in the steady-state mode. The system equations of the original problem are represented in the $(W, \Lambda, K)$-form; for this form, the standard $H_\infty$ optimization problem is stated and solved. The desired accuracy of the system is achieved by analytically assigning the weight matrix of the controlled variables. The controller design method is illustrated by an example of solving a well-known benchmark problem.