We report on very recent work on the stabilization of the steady-state solutions to Navier-Stokes equations on an open bounded domain R C Rd, d = 2,3, by either interior, or else boundary control. More precisely, as to the interior case, we obtain that the steadystate solutions to Navier-Stokes equations on R C Rd, d = 2,3, with no-slip boundary conditions, are locally exponentially stabilizabl...

We consider the problem of boundary feedback stabilization of homogeneous equilibria in unstable fluid mixtures that are governed by unstable linear reaction-convection-diffusion equations. We extend boundary feedback control laws designed for the one-dimensional reaction-diffusion equation using the backstepping method to this higher-dimensional case. We show that, under certain mathematical c...

Conditions for boundary feedback stabilizability of non-uniform linear 2 × 2 hyperbolic systems over a bounded interval are investigated. Themain result is to show that the existence of a basic quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered interval. This result is used to give explicit conditions for the existence of stabilizing...

Conditions for boundary feedback stabilisability of linear 2×2 hyperbolic systems over a bounded interval are investigated. The main result is to show that the existence of a quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered interval. This result is used to give explicit conditions for the existence of stabilising linear boundary fe...

A new approach for pole placement of nonlinear systems using state feedback and fuzzy system is proposed. We use a new online fuzzy training method to identify and to obtain a fuzzy model for the unknown nonlinear system using only the system input and output. Then, we linearized this identified model at each sampling time to have an approximate linear time varying system. In order to stabilize...