Minimum H∞-norm regulation of linear discrete-time systems and its relation to linear quadratic discrete games

A solution is derived to the H_∞-optimization problem that arises in multivariable discrete-time regulation when the controller has full access to the state vector. The solution method is based on the close relations that exist between linear quadratic differential game theory and H_∞-optimization. The existing theory of discrete-time quadratic games is readily applied in order to derive the solution to a finite-time horizon version of the H_∞ -optimization problem. The solution of the infinite-time horizon H_∞-optimization problem is obtained by formally taking the limit of the number of stages to infinity