Complete solution to the nonsingular H∞ four block problem

This paper considers the complete solution to the four block problem in a combined H₂/H_∞ setting. Specifically, an LQG control design problem involving a constraint on the H_∞ disturbance attenuation is addressed. It is shown that the optimal H₂/H_∞ dynamic compensation gains are completely characterized via coupled Riccati/Lyapunov equations. The principal result involves sufficient conditions for characterizing full- and reduced-order controllers that satisfy both H₂/ and H_∞ performance costs. As a special case of this unified result we obtain the full-order H_∞ solution to the general four block optimal control problem and the pure reduced-order H_∞ solution with no H₂/ contribution.