Infinite determinant method for stability analysis of periodic systems

A systematic method for stability analysis of periodic systems using the infinite determinant (ID) approach is presented. It is first shown that, corresponding to every horizontal strip of width 2¿ (2¿ being the pumping frequency) in the complex characteristic exponent plane, there exists an order beyond which the ID truncations continue to have exactly n (n being the system order) zeros in that strip, and that these n zeros converge to the characteristic exponent of the system as the truncation size is increased to infinity. Based on extensive numerical experimentation, a convenient criterion for the minimum order of truncation that ensures sufficient convergence of the zeros is arrived at. The characteristic exponents thus obtained are in excellent agreement with those obtained by the `single-pass¿ STM method. Two methods are developed for the efficient numerical evaluation of the zeros of the ID truncations. The method for the system with cisoidal pumping is computationally superior to the STM method.