The classical discrete-time algebraic Riccati equation (DARE) is considered in the case when the corresponding closed-loop matrix is singular. It is shown that in this case all the symmetric solutions of the DARE coincide along some directions. A parametrization of the set of solutions in terms of the reduced-order DARE is then obtained. This parametrization provides an algorithm (that appears to be computationally very attractive when the multiplicity of the zero eigenvalue of the closed-loop matrix is large) for the computation of the solutions of the DARE. The same issue for the generalized DARE is also addressed.
On the structure of the solutions of discrete-time algebraic Riccati Equation with singular closed-loop matrix
FERRANTE, AUGUSTO
2004
Abstract
The classical discrete-time algebraic Riccati equation (DARE) is considered in the case when the corresponding closed-loop matrix is singular. It is shown that in this case all the symmetric solutions of the DARE coincide along some directions. A parametrization of the set of solutions in terms of the reduced-order DARE is then obtained. This parametrization provides an algorithm (that appears to be computationally very attractive when the multiplicity of the zero eigenvalue of the closed-loop matrix is large) for the computation of the solutions of the DARE. The same issue for the generalized DARE is also addressed.File in questo prodotto:
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