Abstract
This paper considers the mixed-norm H 2/H ∞ standard problem. Specifically, an LQG control design problem involving a constraint on H ∞ disturbance attenuation is addressed. It is shown that the H 2/H ∞ dynamic compensator gains are completely characterized via coupled Riccati/Lyapunov equations. The principal result involves sufficient conditions for characterizing full- and reduced-order controlleers that satisfy bounds on both H 2 and H ∞ performance costs. As a special case of this unified result we obtain the full-order H ∞ solution to the standard control problem the pure reduced-order H ∞ solution with no H 2 contribution. Further extensions include nonstrictly proper dynamics, a direct transmission term from disturbances to H ∞ performance variables, cross-weighting and sensor noise/plant disturbance correlation, and a treatment of the pure reduced-order H ∞ control problem.
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