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This thesis has explored the effects of three variables in thermal biofeedback training using false feedback. The three controlled variables in this study are: knowledge of response for the student experimenter, and training sessions. Knowledge of response refers to the identification of a particular internal response (either GSR or skin temperature) of a subject.Although not statistically significant, results for the knowledge of response variables were found to be in the theoretically predicted direction in all conditions.

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The robustness of the stability property of multivariable feedback control systems with respect to model uncertainty is studied and discussed. By introducing a topological notion of arcwise connectivity, existing and new robust stability tests are combined and unified under a common framework. The new switching-type robust stability test is easy to apply, and does not require the nominal and perturbed plants to share the same number of closed right half-plane poles, or zeros, or both. It also highlights the importance of both the sensitivity matrix and the complementary sensitivity matrix in determining the robust stability of a feedback system. More specifically, it is shown that at those frequencies where there is a possibility of an uncertain pole crossing the jw-axis, robust stability is "maximized" by minimizing the maximum singular value of the sensitivity matrix. At frequencies where there is a likelihood of uncertain zeros crossing the imaginary axis, it is then desirable to minimize the maximum singular value of the complementary sensitivity matrix. A robustness optimization problem is posed as a non-square H^∞-optimization problem. All solutions to the optimization problem are derived, and parameterized by the solutions to an "equivalent" two-parameter interpolation problem. Motivated by improvements in disturbance rejection and robust stability, additional optimization objectives are introduced to arrive at the 'best' solution.

The reach control problem (RCP) characterizes a control design approach, based on computer science notions of object triangulation, that has been extensively developed as a means of guiding the complete transient response of a system, entirely within a desired polytopic region of state-space operation characterized by linear constraints on its states. This thesis expands upon results achieved in the area of RCP problem solvability under continuous feedback, identifying new necessary conditions. It accomplishes this using algebraic topology constructs, mapping the reach control problem to an equivalent topological one to successfully demonstrate conditions under which topological obstructions are generated. These obstructions, which render the RCP unsolvable by continuous feedback are then used to characterize equivalent conditions necessary for solvability of the problem. This thesis also serves to formally demonstrate the substantial advantages of the RCP design approach over more conventional industry techniques, by solving real-world problems with complex specifications.

The reach control problem (RCP) characterizes a control design approach, based on computer science notions of object triangulation, that has been extensively developed as a means of guiding the complete transient response of a system, entirely within a desired polytopic region of state-space operation characterized by linear constraints on its states. This thesis expands upon results achieved in the area of RCP problem solvability under continuous feedback, identifying new necessary conditions. It accomplishes this using algebraic topology constructs, mapping the reach control problem to an equivalent topological one to successfully demonstrate conditions under which topological obstructions are generated. These obstructions, which render the RCP unsolvable by continuous feedback are then used to characterize equivalent conditions necessary for solvability of the problem. This thesis also serves to formally demonstrate the substantial advantages of the RCP design approach over more conventional industry techniques, by solving real-world problems with complex specifications.

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Thesis (PhD)--University of South Australia, 2000