Robust Regional Eigenstructure Assignment for Constrained Second-Order Systems Using Nonlinear Optimization

In this paper, a robust, regional eigenstructure assignment via state feedback control for constrained second-order linear dynamical systems is presented. Starting from a nonlinear optimization approach recently proposed by the authors to assign a given set of desired eigenvalues, the constraints of the optimization problem are adjusted to achieve regional eigenvalue assignment. Furthermore, a multicriteria weighting sum involving the control directions and a bona fide quantity related to the condition number of the left and right eigenvectors is maximized in the cost function. The goals of such cost function are to maximize the size of the invariant polyhedron within the set of state constraints and minimize the global closed-loop eigenvalue sensitivity against uncertainties on the system model matrices. The proposed approach is applied in a benchmark model of flutter control for a wing in an airstream, and the results illustrate the flexibility offered by the new proposed constraints and cost function.