H/sub infinity /-control by state-feedback and fast algorithms for the computation of optimal H/sub infinity /-norms

The suboptimality of some parameter for H/sub infinity /-optimization by dynamic state-feedback is characterized in terms of the solvability of Riccati inequalities. This is done without restricting the finite zero structure of the plant. If there are no system zeros on the imaginary axis, the H/sub infinity /-problem can be treated in a complete and satisfactory way. Explicit characterizations optimum to be achieved are provided, and a closed formula for the optimal value is derived in terms of the H/sub infinity /-norm of some fixed transfer matrix. If the optimum is not attained, any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high-gain. A globally and quadratically convergent algorithm to compute the optimal value is proposed. This algorithm is generalized to the H/sub infinity /-optimization problem by measurement feedback.<
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