Exponential stabilization, via riccati operator, of hyperbolic systems with uncontrolled, unbounded perturbations
In this paper, we shall prove that under some restrictions placed on the system, the sought after stabilizing feedback F can be constructed via the solution to the Algebraic Riccati Equation. We shall establish that for this class of systems, the linear feedbacks given by the Riccati operator produce a robust stabilization in presence of uncontrolled nonlinear and unbounded perturbations. We remark that our abstract model incorporating nonlinear unbounded perturbation is motivated by several applications, arising in control problems for the plate and wave equations with nonlinearly perturbed boundary conditions. Here, the effect of uncontrolled nonlinearities on the boundary is inherently unbounded.
Lecture Notes in Control and Information Sciences
Lasiecka, I. (1991). Exponential stabilization, via riccati operator, of hyperbolic systems with uncontrolled, unbounded perturbations. Lecture Notes in Control and Information Sciences, 154, 102-115. https://doi.org/10.1007/bfb0044487