On the structure of the solution of continuous-time algebraic Riccati equations with closed-loop eigenvalues on the imaginary axis

Abstract

This paper proposes a decomposition of the continuous-time algebraic Riccati equation aimed at eliminating the problem of the presence of closed-loop eigenvalues on the imaginary axis. In particular, we show that it is possible to parameterize the the entire set of solutions of the given Riccati equation in terms of the solutions of a reduced-order Riccati equation, which is associated to a Hamiltonian matrix with no eigenvalues on the imaginary axis, and some free parameters arising from the presence of imaginary eigenvalues of the Hamiltonian matrix.