Geometric Methods in Feedback Control and Parametrization Problems

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This research addresses several related topics of control theory. The first problem is concerned with issues of controllability of linear systems with state and control constraints which is of interest to control engineers when attempting to deal with system elements that can overload or saturate. The second problem of parameterization is important in adaptive control applications when simultaneous control and plant identification is important. Finally, the idea of feedback transformations (linearization) of nonlinear systems in a multivariable setting provides a possible means of controlling certain complicated nonlinear systems.