Robust disturbance attenuation of fluid dynamic systems with norm-bounded uncertainties (Q2711460)

This paper deals with robust \(H_\infty\) control under modelling uncertainty for certain nonlinear fluid dynamical systems described by the Navier-Stokes equations. There are parametric uncertainties (time-dependent and norm-bounded) in all entries. NEWLINENEWLINENEWLINEThe authors use a combination of the Hamilton-Jacobi-Isaacs equations with Riccati equation techniques to design a feedback controller such that the resulting closed-loop system is robustly stable and a prescribed \(H_\infty\) performance is achieved independently of the uncertainties. When the nonlinear feedback gain can be locally approximated by a linear feedback gain, they also construct a suboptimal solution via a fixed state feedback. The results extend previous work by Barbu and Sritharan, where no modelling uncertainty is permitted.