A bilinear optimization-based approach for eigenstructure assignment output feedback control of  second-order linear systems

In this paper, we propose an eigenstructure assignment approach for static-output feedback control design of second-order systems. First, the eigenvalue assignment problem is translated into that of solving coupled Sylvester equations, resulting in a set of bilinear matrix equalities, involving the corresponding left and right eigenvectors. These equalities are used as constraints of bilinear programming problems, for which different cost functions are proposed, representing the numerical conditioning of the solution and sensitivity functions, which serve as a measure of the robustness of the assigned eigenvalues against uncertainties in the system's parameters. The method can be extended to the design of a second-order dynamic output feedback compensator with a suitable number of degrees of freedom for cases where arbitrary eigenvalue assignment is not guaranteed with Kimura's condition or a less conservative one. Numerical examples using two benchmarks are presented to illustrate the effectiveness of the proposed approach.