MODAL CONTROL OF LINEAR PARABOLIC SYSTEMS WITH INTERNAL FEEDBACK LOOP
In this paper, we consider the problem of stabilizing linear parabolic systems with internal feedback by external finite-dimensional controllers. The dynamics of the system is described by the operator where is the infinitesimal generator of an analytic semigroup, Qis a bounded operator whose range is finite-dimensional, and Dis a bounded operator. For the system, we first consider the case of distributed control and distributed observation. We use modal decomposition techniques for the derivation of a finite-dimensional model. Then we use the stability radius theory for the construction of finite-dimensional controllers. Next, we consider the case of distributed control and boundary observation, and also give the construction method of finite-dimensional controllers.
linear parabolic system, distributed control, distributed/boundary observation, stability radius, finite-dimensional controller.