Minimum-Gain Pole Placement With Sparse Static Feedback

The minimum-gain eigenvalue assignment/pole placement problem (MGEAP) is a classical in linear time-invariant systems with static state feedback. In this article, we study the MGEAP when feedback has arbitrary sparsity constraints. We formulate sparse as an equality-constrained optimization and present analytical characterization of its locally optimal solution terms eigenvector matrices closed-loop system. This result used to provide geometric interpretation nonsparse MGEAP, thereby providing additional insights for problem. Furthermore, develop iterative projected gradient descent algorithm obtain local solutions using parameterization based on Sylvester equation. heuristic compute projections, which also provides novel method solve eigenvalue/pole assignment Also, relaxed version presented developed approximately MGEAP. Finally, numerical studies are compare properties algorithms, suggest that proposed projection converges most cases.