The Stabilizing Solution of the Algebraic Riccati Equation

Authors

B. P. Molinari

Year

1973

Journal Paper

Algorithm

Stabilizing Solution of the Algebraic Riccati Equation

Source

SIAM Journal on Control

Identifiers

DOI 10.1137/0311021

Abstract¶

This paper investigates solutions Xhat of the algebraic Riccati equation F'X + XF - XGG'X + Q = 0 with the property Re lambda(F - GG'Xhat) <= 0. The uniqueness and existence of such a solution is completely characterized. In addition, the conditions are strengthened to characterize the important stabilizing solution (Re lambda(F - GG'Xhat) < 0). All standard existence results are recovered as special cases.

Summary¶

Characterizes the stabilizing solution of the algebraic Riccati equation arising in LQR design, establishing necessary and sufficient conditions for its existence and uniqueness. A key reference for the theoretical foundations of Riccati-based optimal control synthesis.