The strongly H/sup /spl infin// stabilization problem is the problem of finding a strictly bounded real controller such that the resulting closed-loop transfer function is also strictly bounded real. Such problems can arise as equivalent problems in the simultaneous stabilization of two or more plants by a single controller such that each closed-loop transfer function has a H/sup /spl infin// norm less than a given performance level. We present a condition in the form of solutions to two AREs to solve the strongly H/sup /spl infin// stabilization problem.