  It has been realized in recent years that coupled focusing lattices in
accelerators and storage rings have significant advantages over conventional
uncoupled focusing lattices, especially for high-intensity charged particle
beams. A theoretical framework and associated tools for analyzing the spectral
and structural stability properties of coupled lattices are formulated in this
paper, based on the recently developed generalized Courant-Snyder theory for
coupled lattices. It is shown that for periodic coupled lattices that are
spectrally and structurally stable, the matrix envelope equation must admit
matched solutions. Using the technique of normal form and pre-Iwasawa
decomposition, a new method is developed to replace the (inefficient) shooting
method for finding matched solutions for the matrix envelope equation.
Stability properties of a continuously rotating quadrupole lattice are
investigated. The Krein collision process for destabilization of the lattice is
demonstrated.
