Optimization of Linear Multivariable Systems with Structured Perturbations and Prescribed Closed-Loop Eigenvalues

M.S. Ibbini and W.F. Swedan


Optimization, multivariable, sensitivity reduction, prescribed eigenvalues, poles placement, LQR


In this article the conventional linear quadratic regulator (LQR) problem is modified to include a third term penalizing state trajectory deviations. The modification is motivated by the tendency of system parameters to assume different values rather than their nominal ones due to components aging, number truncation, and other factors. The proposed optimal controller not only results in an explicit solution to the modified LQR problem, but also allows the designer to assign the closed-loop eigenvalues to prespecified locations. The proposed controller permits the designer to consider undesired variations in both system matrices (A, B) and also to assign the closed-loop eigenvalues to some desired locations. This eigenvalues assignment is achieved without imposing any restriction either on their nature, multiplicity, or their open- or closed-loop locations in the complex plane.

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