Finite horizon static output H_∞ control with automatic beam guidance application

The problem of designing static output-feedback controllers for finite time horizon is considered. The design problem is solved in two settings: one is the pure H_∞ setting where the disturbance attenuation problem is solved, and the other is a mixed H₂/H_∞ setting where an upper bound on the L₂ norm of the error is minimized as well. In the pure H_∞ setting, a single Riccati-like equation should be solved, where the required projection matrix is obtained up to a free parameter. In the other setting, a two-point boundary-value problem has to be solved. The theory of the mixed H₂/H_∞ setting is illustrated by a design of an automatic lateral beam guidance controller.