In the present paper we obtain a closed-form solution for the class of continuous-time algebraic Riccati equations (AREs) with vanishing state weight. The AREs in such a class solve a minimum energy control problem. The present work extends on previous preliminary results by considering the more challenging case of repeated unstable eigenvalues. The obtained closed-form solution gives insight on issues such as loss of controllability and it might also prove comparable in terms of numerical precision over current solving algorithms.
2010 American Control Conference, (ACC 2010). Proceedings of the 2010 American Control Conference (Baltimore, MD 30 June - 2 July, 2010) p. 1111-1116