Partial Strong Stabilization of Semi-Linear Systems and Robustness of Optimal Control

This work addresses the idea of optimal stabilization, namely robustness of optimal stabilization with nonlinearity Lipschitz of distributed semilinear systems using bounded control. This problem is treated under the condition of the unbounded operator, we show that the system is stable once the exact observability assumption is executed together with a Lipschitz property of the nonlinear operator. The concept of bounded control is also investigated in realistic domain. The stabilizing feedback is characterized by the minimization of the problem of cost. We also give different applications to parabolic and hyperbolic equations.