LMI-based synthesis for controlling periodic solutions in a class of nonlinear systems

The paper considers the problem of designing controllers to stabilize periodic orbits in a class of sinusoidally forced nonlinear systems. This problem is formulated as an absolute stability problem of a linear periodic feedback system, in order to employ the well-known circle criterion. In this setting, we provide an LMI-based synthesis of the optimal stabilizing controller, i.e., the one ensuring the largest obtainable stability bounds.