H-INFINITY-OPTIMAL CONTROL FOR SINGULARLY PERTURBED SYSTEMS .2. IMPERFECT STATE MEASUREMENTS

In this paper we study the H(infinity)optimal control of singularly pe rturbed linear systems under general imperfect measurements, for both finite- and infinite-horizon formulations. Using a differential game t heoretic approach, we first show that as the singular perturbation par ameter (say, epsilon > 0) approaches zero, the optimal disturbance att enuation level for the full-order system under a quadratic performance index converges to a value that is bounded above by (and in some case s equal to) the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate ''slow'' and ''fast '' quadratic cost functions, with the bound being computable independe ntly of epsilon and knowing only the slow and fast dynamics of the sys tem. We then construct a controller based on the slow subsystem only a nd obtain conditions under which it delivers a desired performance lev el even though the fast dynamics are completely neglected. The ultimat e performance level achieved by this ''slow'' controller can be unifor mly improved upon, however, by a composite controller that uses some f eedback from the output of the fast subsystem. We construct one such c ontroller, via a two-step sequential procedure, which uses static feed back from the fast output and dynamic feedback from an appropriate slo w output, each one obtained by solving appropriate epsilon-independent lower dimensional H(infinity)-optimal control problems under some inf ormational constraints. We provide a detailed analysis of the performa nce achieved by this lower-dimensional epsilon-independent composite c ontroller when applied to the full-order system and illustrate the the ory with some numerical results on some prototype systems.