LOCALLY DISTRIBUTED CONTROL AND DAMPING FOR THE CONSERVATIVE-SYSTEMS

In this paper we note the equivalence between exact controllability an d exponential stabilizability for an abstract conservative system with bounded control. This enables us to establish a frequency domain char acterization for the exact controllability/uniform exponential decay p roperty of second-order elastic systems, such as the wave equation and the Petrovsky equation, with (locally) distributed control/damping. A piecewise multiplier method for frequency domain is introduced. For s everal classes of PDEs on regions which are not necessarily smooth, we obtain a sufficient condition for the subregion on which the applicat ion of central/damping will yield the exact controllability/uniform ex ponential decay property. This result provides useful information for designing the location of controllers/dampers for distributed systems with a law of conservation.