Robust Control of Multivariable Systems Subject to Structured Real Parameter Variations

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This research deals with the problem of analysis, synthesis and design of control systems when the plant is subject to perturbations of a set of real physical parameters. This type of model occurs in robotics, chemical processes, aircraft control, large space structures and many other engineering systems. Such plants are called structured real parameter (SRP) plants. For linear time-invariant multivariable SRP systems the following problems will be considered: (1) determination of a robustness measure for a given controller. One candidate for such a measure is the size (radius) of the stability hypersphere in parameter space. The theory and computational algorithm for determining this radius will be investigated. (2) The development of a procedure for the sythesis of a controller that robustifies, i.e. maintains closed loop stability of the system against a given set of ranges of plant parameter excursions. This requires a generalization and the development of a sythesis version of the type of results developed by Kharitonov. (3) The development of design procedures for maximal robustness by choosing the free controller parameters to maximize the robustness measure. (4) The formulation and solution of the problem of trading off robustness against deviations from the desired response measured suitably and optimized over the controller parameters.