This paper presents the indirect state H∞ control approach to a multidimenslOnal bifurcation system of actual engmeermg with non-semisimple double zero value , based on the nonlinear H∞ control theory. U nder some conditions , parametenzatlOn formulas of all controllers are derived. The solution of the problem is shown to be related to the eXlstence of solutions of a palr of Hamilton-Jacobi equatlOns , which are assoclated with parameters and state feedback , respectively.