Robust stabilization of singular systems with \(H_\infty\)-bounded uncertainty (Q1287047)

The paper considers stabilization of a linear time invariant system, which is singular, namely of the form \[ E\dot x= Ax+ Bu,\quad y= Cx. \] It is assumed, naturally, that \(\text{det}(sE- A)\) is not identically zero. The stabilization is supposed to be robust with respect to a family of singular systems with perturbations. A characterization of robust stabilization is provided, and an estimate for the robust stability bound is computed. A concrete example accompanies and illustrates the abstract considerations.