Nondifferentiable design optimization involving the eigenvalues of control system matrices
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The designer of linear dynamic systems is always concerned with their eigenvalues because of such important issues as stability, reaction speed, robustness etc. Mathematical programming has proved to be a powerful instrument for control systems design. Requirements upon eigenvalues can also be formulated as part of the design optimization problem. This paper presents a nondifferentiable approach for solving such problems. It considers the general case when the system matrices are non-symmetric. The approach is based on the numerical calculation of the Jordan canonical form and on the generalized gradients of F.Clarke. An algorithm was developed and implemented. Finally, some control systems design examples illustrate the features of the considered problems and approaches.
KeywordsDescent Direction Control System Design Design Optimization Problem Elementary Divisor Multiple Eigenvalue
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