Output Feedback Stabilizing Control With an H_∞ Bound on Disturbance Attenuation

This paper considers the design of direct output static and dynamic stabilizing controllers for linear systems. Here, the controllers that stabilize the closed-loop system must satisfy an H_∞ disturbance attenuation constraint. Sufficient conditions for the existence of such controllers are presented in the form of two coupled nonlinear matrix equations. These conditions are derived by solving a mixed-norm H₂/H_∞ optimal control problem. The solution of these equations via a continuation method is also presented. Using the solution algorithm, a fixed order stabilizing controller gain matrix that minimizes the H_∞ norm of the closed-loop transfer function can be computed. The controller design technique is applied to the vertical dynamics of an aircraft. It is shown that the performance of the reduced order controllers designed using the technique proposed in this paper is superior to that of full order controllers obtained using the standard LQG approach.