A generalized eigenproblem approach to singular control problems. II. H/sup infinity / problems
Brian R. Copeland, Michael G. Safonov · 2005
For Pt.I, see Proc. IEEE Conf. on Decision and Control, 1991. A descriptor system representation is given for control laws for singular H/sup infinity / problems in terms of the generalized eigenstructure of the two Hamiltonian system matrix pencils associated with the two H/sup infinity / Riccati equations. The new formulation allows for the solution of singular H/sup infinity / problems involving plants for which D/sub 12/ and D/sub 21/ are not full rank and which have jw-axis zeros. Additionally, examination of the solution indicates how to take advantage of rank deficiencies of D/sub 12/ and D/sub 21/ so as to obtain H/sup infinity / 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/sup infinity / control law formula which applies with equal ease to both singular and nonsingular H/sup infinity / control problems.>