Feedback Stabilization of du/dt =Au + Bf in Hilbert Space When the Normalization Function is < or = r

摘要

This paper considers the feedback stabilization of a linear control system in an infinite dimensional state space. However unlike the standard feedback control problem where the goal is to find a linear feedback control law, we restrict ourselves to the case where the controls f(t) satisfy a certain priori constraint. The author derives such a nonlinear feedback law based on energy stability methods. The analysis of the asymptotic behavior of the state u(t) is based on the theories of nonlinear evolution equations and contraction semigroups. While an earlier paper treated related problem of sub-optimal control the results given here on feedback stabilization are new. A related optimal control problem was considered by Barbu.