Output feedback robust \(H \infty\) control with \(D\)-stability and variance constraints: Parametrization approach
The problem of robust \(H_\infty\) controller design for uncertain continuous-time systems with variance and \(D\)-stability constraints is considered. The parameter uncertainties are allowed to be unstructured but norm-bounded. The aim of this problem is the design of an output feedback controller such that, for all admissible uncertainties, the closed-loop poles are placed within a specified disk, the \(H_\infty\) norm bound constraint on the disturbance rejection attenuation is guaranteed, and the steady-state variance for each state of the closed-loop system is no more than the prescribed individual upper bound, simultaneously. Reviewer's remark: The paper contains an essential drawback, which frequently appears in mathematical papers devoted to similar problems. Namely, no nonzero external signals which for instance determine some nonzero reference or disturbance signals are considered. The result is that the obtained control law can not be applied in the system with nonzero reference signal in this manner that it assures the assumed steady-state error. This is exactly seen in the numerical example described in the paper, in which the obtained gains \(K\) of control law are to small to assure sufficiently small steady state errors. In practice not only the robust stability but also the accuracy of steady state is important, and both these problems must be considered in parallel. Therefore the meaning of the papers which consider only the robust stability without steady state accuracy is very limited from application point of view.
scientific article; zbMATH DE number 2171978
scientific article