ROBUST EIGENVALUE ASSIGNMENT WITH MAXIMUM TOLERANCE TO SYSTEM UNCERTAINTIES

For a linear time-invariant system with a feedback controller, the closed-loop eigenvalues perturb due to system uncertainties. Given an allowable tolerance for the closed-loop eigenvalue perturbation, an algorithm is developed to obtain a state feedback controller that maximizes the uncertainty tolerance of the open-loop system matrix. The design procedure is based on an existing eigenvalue assignment technique using Sylvester's equation. A robustness condition is derived to guarantee satisfaction of a specified closed-loop perturbation tolerance. Finally, an iterative algorithm is presented for easy numerical implementation to compute the robust controller, and a numerical example is given for illustration.