A general H∞/LTR design problem

An alternative approach to the loop transfer recovery (LTR) design problem based on H_∞ optimization is considered. An H_∞/LTR design problem is formulated as an H_∞ optimization of the weighted recovery matrix (RM). This general recovery formulation includes the indirect H_∞/LTR design problem (equivalent to LQG/LTR), the H_∞/LTR sensitivity, and the input-output recovery problem as special cases. The weight matrix is also used for obtaining robustness in the final design. The control problem corresponding to the general H_∞ /LTR design problem is formulated as a standard H_∞ state-space problem. The state-space solution to the H_∞ problem is derived and the corresponding H_∞/LTR controller is implemented as a Luenberger observer of order at most n+n_w (n_w is the order of the weight on the RM). The proposed H_∞/LTR method handles both minimum phase and nonminimum phase systems in the same framework