Exploiting Semi-Separable and toeplitz structure in distributed control of homogeneous systems with arbitrary boundary conditions

We consider the problem of designing controllers for distributed systems consisting of N subsystems connected in a string. In the past, computationally efficient techniques have been separately developed for finite length completely heterogeneous systems and doubly infinite completely homogeneous systems. In this paper we show how the ordinarily O(N) Sequentially Semi Separable(SSS) controller synthesis techniques can be specialized to an intermediate case: finite length homogeneous systems with boundary conditions, resulting in controller synthesis routines with computational complexity independent of N. As an example, these techniques are used to compute an H₂ controller for a heat conduction problem.