Optimal synthesis of state-estimate feedback controllers with minimum l2-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.