State-space approach to control design under partial statistical information for exogenous signals (Q1576516)

The aim of the paper is to consider control problems where the objective is to minimize the worst-case variance of the regulated output in the class of all exogenous signals that meet partially specified statistical information. State-space results for analysis and state feedback design are presented using finite-dimensional convex optimization problems of the max-min type where the inner minimization problem involves linear matrix inequalities, while the output feedback problem involves a bilinear matrix inequality. The investigation is based on properties of strictly positive real transfer functions. Using signal theoretic ideas the authors derive useful insights about the structure of the worst-case signal.