Enhancement of stability of linear parabolic systems by static feedback (Q1861789)

The author considers a linear parabolic distributed parameter system in a Hilbert space \(H\) under static feedback, \[ u'(t) + Lu(t) = \sum_{k=1}^n \langle u(t), w_k \rangle h_k. \] The problem is to enhance the exponential stability of the system by suitable selection of the sensors \(w_k\) and the actuators \(h_k,\) in the presence of spillovers of the \(w_k\) and \(h_k\).