Decentralization properties of optimal distributed controllers

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are fully distributed over the spatial coordinate. For such systems and quadratic optimization criteria (LQR, /spl Hscr//sub 2/, /spl Hscr//sub /spl infin//) the optimal control problem can be solved by diagonalization based on Fourier analysis over the spatial domain, yielding a parameterized family of Riccati equations over spatial frequency. By applying analytic continuation methods to the Riccati equation, we provide methods to estimate the spatial decay rate of the convolution kernel for the optimal controller. In addition, quantitative measures of controller decentralization in terms of spatial moments are presented.