The Riccati-based approach to robust control is completely understood in theory since long but seldom used for large-scale systems in practice. Only recently, we have transferred iterative algorithms that allow the computation of solutions to LQR Riccati equations in the large-scale setting to the indefinite Riccati equations that appear in robust control. For descriptor systems, the relevant Riccati equations are nonsymmetric and, for large-scale systems, there is no established algorithm that can handle these even in the LQR case.
In this paper, we show how the general theory for descriptor systems with index-1 pencil coincides with the theory for standard linear time invariant case with feedthrough terms. This provides an algorithm to characterize and to compute the solution to the generalized indefinite Riccati equations via standard Riccati equations. In view of feasibility for large-scale descriptor systems, we illustrate how to arrive at the equivalent standard Riccati-equation without resorting to the canonical form used in the derivation of the theoretical results.