A perturbation approach to the H2 analysis of spatially periodic systems

We consider a class of spatially distributed systems with spatially periodic coefficients. Frequency domain methods are used to convert a linear system belonging to this class into a family of infinite-dimensional LTI ones. The frequency and amplitude of the periodic coefficients are then treated as parameters. A perturbation analysis is then performed on the amplitude of the periodicity to find a computationally efficient method of calculating the H² -norm. The dependence of the H²-norm on the amplitude and frequency of the periodic coefficients is demonstrated.