Optimal Synthesis of State-Estimate Feedback Controllers With Minimum $l_{2}$ -Sensitivity

This paper investigates the problem of synthesizing the optimal structure of a state-estimate feedback controller with minimum l ₂-sensitivity and no overflow. First, the l ₂-sensitivity of a closed-loop transfer function with respect to the coefficients of a state-estimate feedback controller is analyzed. Next, two iterative techniques for obtaining the coordinate transformation matrix which constructs the optimal structure of a state-estimate feedback controller are developed so as to minimize an l ₂-sensitivity measure subject to l ₂-scaling constraints. One technique is based on a Lagrange function, some matrix-theoretic techniques, and an efficient bisection method. Another technique converts the problem into an unconstrained optimization formulation by using linear-algebraic techniques, and optimizes it by applying an efficient quasi-Newton method with closed-form formula for gradient evaluation. A numerical example is also presented to illustrate the utility of the proposed techniques.