A generalized eigenproblem approach to singular control problems. II. H∞ problems

For Pt.I, see Proc. IEEE Conf. on Decision and Control, 1991. A descriptor system representation is given for control laws for singular H^∞ problems in terms of the generalized eigenstructure of the two Hamiltonian system matrix pencils associated with the two H^∞ Riccati equations. The new formulation allows for the solution of singular H^∞ problems involving plants for which D₁₂ and D₂₁ are not full rank and which have jw-axis zeros. Additionally, examination of the solution indicates how to take advantage of rank deficiencies of D₁₂ and D₂₁ so as to obtain H^∞ control laws of reduced order. The derivations for the singular case involve perturbing the singular problem to a nearby nonsingular problem, then analyzing the limiting behavior of the control law as the perturbation vanishes. The result is a numerically robust H^∞ control law formula which applies with equal ease to both singular and nonsingular H^∞ control problems