Partial Singular Value Assignment for Large-Scale Systems

The partial singular value assignment problem stems from the development of observers for discrete-time descriptor systems and the resolution of ordinary differential equations. Conventional techniques mostly utilize singular value decomposition, which is unfeasible for large-scale systems owing to their relatively high complexity. By calculating the sparse basis of the null space associated with some orthogonal projections, the existence of the matrix in partial singular value assignment is proven and an algorithm is subsequently proposed for implementation, effectively avoiding the full singular value decomposition of the existing methods. Numerical examples exhibit the efficiency of the presented method.