An algebraic approach to discrete-time H∞ control problems

The H_∞ (sub)optimal control problem that arises in multivariable discrete-time control system design is solved. A solution to the problem is carried out by iteratively solving two algebraic Riccati equations. A simple proof is provided. This yields state-space formulae for synthesis of a suitable observer-based controller whose order is equal to that of the given plant. The results are also applied to the robust stabilization of linear discrete-time systems including time-varying uncertain parameters. A numerical example is given to show validity of the approach.