this paper, the standard four block 'H" control problem of dis- crete time systems is solved by using a. J-lossless embedding ap- proach. The result shows that the four block 3-1" control problem of discrete time systems has a solution iff the solutions of two dis- crete Riccati equations a.re positive semidefinite and the spectral radius of their product, is less than the prescribed norm bound. However, as the reflection of the discrete time character, an ad- ditional condition is required for the solvability of discrete time 3-1" control problems. The parametrization of all 31" controllers is derived. Moreover, in contrast with many previous works, our approach is direct and the conventional model-matching formula- tion is bypassed. The convent,ional assumption on discrete time systems that the A-ma.trix be nonsingular is gotten around by us- ing the descriptor form. Any unnecessary assumption on B1, Cl is lifted by a spectrum decomposit.ion argument.
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