Riccati-based feedback stabilization of incompressible Navier-Stokes models via reduced-order modelling by iterative rational Krylov algorithm

Due to the system structure and memory requirement, stabilization of higher dimensional incompressible NavierStokes models is always a very challenging task. The conventional simulation techniques are time laborious, sparsity exploiting, and contain complex matrix-vector formulations. To bypass those infeasibilities, we are proposing a modified sparsity-preserving Iterative Rational Krylov Algorithm (IRKA) based projection technique for Riccati-based feedback stabilization of incompressible Navier-Stokes models via reduced-order modelling. In this work, reduced-order matrices and hence reduced-order feedback matrices will be used to attain the optimal feedback matrix for the target models through the inverse projection scheme. In the numerical validation, graphical approaches to the measures of transient behaviors are included. The accuracy of the work is justified by the H
2
-norm optimality.