Solving algebraic Riccati equation for singular system based on matrix sign function

The objective of this paper is to propose a constructive methodology for determining the appropriate weighting matrices {Q, R}, which guarantees the solvability of the generalized algebraic Riccati equation and for solving the generalized Riccati equation via the matrix sign function for the stabilizable singular system. A decomposition technique is developed to decompose the singular system into a controllable reduced-order regular subsystem and a non-dynamic subsystem. As a result, the well-developed analysis and synthesis methodologies developed for a regular system can be applied to the reduced-order regular subsystem. Finally, we transform the results obtained for the reduced-order regular subsystem back to those for the original singular system. Illustrative examples are presented to show the effectiveness and accuracy of the proposed methodology.