Patent ID: 7693693

Claim:
A method comprising: determining a set of solutions for an output feedback pole placement problem based on parameters of a physical system, the solutions being stable and well-conditioned to permit changes to the parameters of the physical system to be monitored; adjusting the physical system based on the solutions determined; acquiring updated parameters of the physical system; determining a set of updated solutions for the output feedback pole placement problem based on the updated parameters of the physical system; and, performing at least one of: adjusting the physical system based on the updated solutions determined; notifying system manager of updated solutions or updated parameters; monitoring changes in the physical system based on the updated solutions determined; and, detecting potentially critical changes in the physical system based on the updated solutions determined, wherein determining the set of solutions comprises determining the set of solutions for a classical, static-output feedback pole placement problem based on the parameters of the physical system by: a) selecting a starting point for determining a solution based on the parameters of the physical system; b) determining the solution based on the starting point, assuming that the parameters are constant, based on a projective approach; c) storing for the solution, a solution matrix, eigenvalues of the solution matrix, one or more final matrices of a solution path of iterations leading to the solution, and eigenvalues of each final matrix of the solution path of the iterations leading to the solution; and, d) repeating a), b), and c) with different starting points for a number of times, such that the set of solutions are distinct; verifying the stability of the solution by: determining a condition number for the solution matrix for the solution; and, determining distances of one or more smallest of the eigenvalues of the solution matrix from an origin; selecting the set of solutions and matrices of the solutions that are well-conditioned, such that the set of solutions are stable under perturbations, and where the one or more smallest of the eigenvalues of the matrices have distances from the origin such that the solutions corresponding to the matrices having the one or more smallest of the eigenvalues have a likelihood of undergoing a change in matrix rank that is below a threshold.