Abstract: In this paper, the problem of second buckling of the spherical shallow shell is calculated by use of the method of progressing step by step and integrating. The result is more exact than that of first approximate analysis for over-critical deformation of spherical shallow shell. It has been solved that the solution of second approximate analysis in this problem can’t be found. The calculating example in this paper shows that the solution of progressing step by step and integrating converges to second approximate solution.

Key words: H_∞ control, decentralized control, modal synthesis, generalized Rayleigh quotient, extended Wittrick-Williams algorithm