Damping feedback stabilization for cyclic interconnections systems: Oscillations suppression and synchronization

This paper considers the problem of stabilizing nonlinear systems in the form of cyclic interconnections. This class of systems is of interest in process control, as some (bio)chemical reactions can be described as cyclic interconnections. The objective of the paper is to present a constructive approach to compute a dissipative potential function for the system. This potential is then used for constructing a smooth feedback stabilizing controller. We first obtain a characteristic one-form for the system by taking the interior product of a non vanishing two-form with respect to the drift vector field. A homotopy operator is then constructed locally around the desired equilibrium, leading to the computation of a dissipative potential for the system. The dynamics of the system is then decomposed into an exact part and an anti-exact one. The exact part is generated by a potential, that is used to construct a smooth stabilizing feedback controller under the weak Jurdjevic–Quinn conditions. We consider the problems of oscillations suppression and synchronization of oscillators as illustrations of potential applications of the proposed construction. The potential of the method is illustrated through an example of a system given as a cyclic interconnection.

► We study stabilization of systems modeled by cyclic interconnections.
► A damping feedback controller is derived from the construction of a Jurdjevic–Quinn potential.
► The approach is used for oscillations suppression and synchronization of control affine cyclic systems.