![]() ![]() Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. In the process, explicit connections are made between mixed mu and absolute stability theory. The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. Robust control design with real parameter uncertainty using absolute stability theory. Our experiments show that this new approach is effective in extending the applicability range of the turbidity methodology and increasing measurement accuracy. ![]() ![]() By using the T-matrix method, we present a robust solution for evaluating the extinction cross section of doublets formed in the aggregation. The evaluations of the rate constants by all previous theories become untenable as the size parameter increases and therefore hampers the applicable range of the turbidity measurement. We attribute this problem to the imperfection of these theories in describing the light scattering from doublets through their evaluation of the extinction cross section. ![]() When the size parameter alpha = 2pi a/lambda > 3, the rate constant data from previous theories for fixed-sized particles show significant inconsistencies at different light wavelengths. The existing theories dealing with the evaluation of the absolute coagulation rate constant by turbidity measurement were experimentally tested for different particle-sized (radius = a) suspensions at incident wavelengths (lambda) ranging from near-infrared to ultraviolet light. Study on improving the turbidity measurement of the absolute coagulation rate constant. ![]()
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