In this paper, we revisit structure exploiting SDP solvers dedicated to the
solution of Kalman-Yakubovic-Popov semi-definite programs (KYP-SDPs). These
SDPs inherit their name from the KYP Lemma and they play a crucial role in e.g.
robustness analysis, robust state feedback synthesis, and robust estimator
synthesis for uncertain dynamical systems. Off-the-shelve SDP solvers require
O(n6) arithmetic operations per Newton step to solve this class of problems,
where n is the state dimension of the dynamical system under consideration.
Specialized solvers reduce this complexity to O(n3). However, existing
specialized solvers do not include semi-definite constraints on the Lyapunov
matrix, which is necessary for controller synthesis. In this paper, we show how
to include such constraints in structure exploiting KYP-SDP solvers.Comment: Submitted to Conference on Decision and Control, copyright owned by
iee