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DAHLEH, MUNTHER ABDULLAH 2007-05-09T19:44:04Z 2007-05-09T19:44:04Z 1987 DAHLEH, MUNTHER ABDULLAH. "DESIGN OF MULTIVARIABLE FEEDBACK CONTROLLERS: ITALIC-L(1)-OPTIMAL SYSTEMS." (1987) Diss., Rice University. <a href="https://hdl.handle.net/1911/16046">https://hdl.handle.net/1911/16046</a>. https://hdl.handle.net/1911/16046 THESIS E.E. 1987 DAHLEH This thesis treats the following problem: Given a multivariable linear time-invariant plant, we want to design a feedback controller in such a way that the closed loop system is internally stable and the output tracks an arbitrary set of bounded and persistent inputs for all time. This problem is equivalent to finding the feedback controller that minimizes the $l\sp{1}$-norm of the impulse response of the error transfer function. A parametrization of all stabilizing feedback controllers in terms of one free stable function is first obtained. This function is then chosen to minimize the norm of the error transfer function. Employing the duality theory in optimization, this problem is converted to a finite dimensional programming problem. In discrete-time systems, optimal solutions are obtained by solving linear programming problems and sets of linear equations. This result, together with the fact that optimal solutions are always rational, implies that this problem is of great practical significance. In continuous-time systems, optimal solutions are generally irrational and thus their implementation is a more difficult task. It is shown that this problem is well suited for designing robust systems when the plant is perturbed by additive or multiplicative stable perturbations, possibly nonlinear. Hence, robustness can be included in the optimization problem and the resulting solutions will have much better overall properties. application/pdf eng Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. Electronics Electrical engineering DESIGN OF MULTIVARIABLE FEEDBACK CONTROLLERS: ITALIC-L(1)-OPTIMAL SYSTEMS Thesis Text Electrical Engineering Engineering Rice University Doctoral Doctor of Philosophy open.access