| This dissertation studies the application of a novel control technique generalized sampled-data hold functions (GSHF)--to the control of multi-input multi-output (MIMO), linear time-invariant systems with structured plant uncertainties. We extend the existing GSHF techniques in three directions: the use of multiple hold functions, the use of GSHF hold together with a dynamic compensator and the adaptation of the GSHF controller. These techniques are used to tackle three control problems, each corresponding to a different level of uncertainty structure: simultaneous controller design, gain margin improvement and adaptive control of plants with parametric uncertainty.;First, when the plant uncertainty is represented by a finite number of distinct possible plant models, we apply GSHF to the simultaneous design problem. We give solutions in three aspects: simultaneous stabilization, simultaneous optimal quadratic performance, and simultaneous pole assignment in combination with simultaneous intersampling performance. Examples are given to illustrate specific design guidelines.;Second, we consider another simple type of plant uncertainty represented by an unknown scalar gain factor--the gain margin problem. We show that for a MIMO continuous-time plant, a GSHF controller can be designed to achieve an arbitrarily large closed-loop gain margin by appropriate selection of the sampling period. This result differs from those in the literature in that the controller we use is a memoryless periodic hold function which feeds back directly the plant output and does not increase the McMillan degree of the closed loop.;Third, when the plant uncertainty is represented by a compact set of unknown plant parameters, we present a parameter adaptive GSHF control scheme with controller pre-scheduling. This control scheme not only updates on-line the dynamic compensator but also updates the GSHF hold function as well. Existence of a finite pre-scheduling set of stabilizing GSHF controllers is proven. Global convergence of the algorithm is established for a general class of systems with the requirement of persistent excitation. Examples are also given. |
