Complete solution to the standard H∞ control problem of discrete-time systems

The standard four block H^∞ control problem of discrete-time systems is solved by using a J-lossless embedding approach. It is shown that the four block H^∞ control problem of discrete-time systems has a solution if the solutions of two discrete Riccati equations are 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 additional condition is required for the solvability of discrete-time H^∞ control problems. The parametrization of all H^∞ controllers is derived. The approach is direct and the conventional model-matching formulation is bypassed. The conventional assumption on discrete-time systems that the A-matrix be nonsingular is avoided by using the descriptor form. Any unnecessary assumption on B₁, C₁ is lifted by a spectrum decomposition argument