A new design of reduced-order controllers for singular H∞ control problems based on ARE approach

Reduced-order controllers for singular H_∞ control problems with infinite zeros are studied via the ARE (algebraic Riccati equation) approach. First, we analyze the relation between the eigenstructure corresponding to the infinite zeros and the parameterization of H_∞ controllers given in the descriptor form. Next, we propose a method to choose appropriately the free parameter in the parameterization for constructing the H_∞ controllers whose orders are equal to the size of a reduced-order ARE involved in solvability conditions of the singular H _∞ control problems. The parameterization of the reduced-order H_∞ controllers is also discussed