Synthesizing H ∞‐controllers for multidimensional systems with given accuracy and degree of stability

We consider linear multidimensional systems with output controllers subject to external perturbances from the class of polyharmonic functions with unknown amplitudes and bounded powers. We formulate the synthesis problem for continuous and discrete output controllers that guarantee a given accuracy with respect to the object’s controlled variables. We introduce the notion of a stabilized state radius of the closed system with respect to controlled variables and reformulate the problem of guaranteeing a given accuracy as a problem of guaranteeing the necessary or minimal possible stabilized state radius. Controller synthesis reduces to a standard H ∞‐problem of suppressing external perturbances, and its numerical solution is based on the linear matrix inequalities (LMI) approach implemented in the MATLAB package LMI Control Toolbox. We show a way to take into account a given degree of stability of the closed system which determines control time. We show a sample controller synthesis for an interconnected electric drive.