H^∞ Optimal control

Abstract

The problem is considered of bounding the H ^∞-norm of the transfer function T _y1u1 relating the output y ₁ to the input u ₁ for the feedback configuration shown in Fig. 1, subject to the closed-loop system being internally stable. A new criterion for internal stability is derived in terms of the Q-parameterization, where Q=K(I + P₂₂ K)^-1. By means of such a stability theory, it is shown that the H ^∞ control problem can be decomposed into two one-sided model-matching problems of the form considered in Part 1 (Hung 1989) of the paper. A closed-form state-space solution with a tight McMillan degree bound is obtained for H ^∞ optimal or suboptimal controllers. An iterative algorithm for obtaining the H ^∞ optimal controller is provided. Computationally, the algorithm requires the solution of only two algebraic Riccati equations in each iteration for which the upper bound on ∣∣T _y1u1∣∣_∞ is adjusted.