Design of H∞ Controllers under Parametric Uncertainty and Power-Bounded External Disturbances

We consider robust stabilization of linear MIMO systems, whose physical parameters are allowed to deviate from the nominal ones within known bounds, and the control plant is subjected to unknown power-bounded polyharmonic external disturbances (with unknown amplitudes and frequencies). The problem is to design a robustly stabilizing controller such that the prespecified errors for the controlled variables in steady state are guaranteed. The solution is based on the “loop-breaking technique” of the plant-controller system with respect to the physical parameters, e.g. Chestnov (1999); it reduces to the standard H∞-optimization procedure by properly choosing the weighting matrix at the controlled variables. This approach is implemented numerically in the MATLAB-based Robust Control Toolbox (RCT).