A new robust controller for linear systems with arbitrarily structured uncertainties

The design of robust controllers for linear single-input-single-output (SISO) systems with uncertainties due to modeling errors and disturbances is considered. It is assumed that a nominal state-space model as well as quantitative bounds on system uncertainties are given. No structural condition such as the matching condition is imposed on system uncertainties. However, it is assumed that the system is minimum phase. Under these assumptions, a controller that achieves regulation of the system output and ensures boundedness of the system state is developed. When the relative degree of the system is larger than two, the controller is first obtained in an unrealizable form, and then its approximation in realizable form is presented. The controller in the approximation form is verified to be effective by a computer simulation study