Animal locomotion can be energy efficient because rhythmical body movements exploit resonance, exchanging elastic or potential energy and kinetic energy. The rhythmical movements of animals are generated by biological oscillators called central pattern generators (CPGs). Coupling structures between body dynamics and a CPG are largely unknown, and how sensory signals are used in a CPG remains an open problem. This research investigates mechanisms underlying entrainment of CPGs to natural oscillations of mechanical systems through sensory feedback. The dynamics associated with animal locomotion consists of two systems: one is an oscillatory system and the other is a rectifier system which converts the rhythmical movements into propulsive force for a desired velocity of locomotion. To reveal the natural entrainment mechanism, we ignore the rectifier system and consider the closed-loop system comprising a linear oscillatory system and a simple CPG, called the reciprocal inhibitory oscillator (RIO). In particular, an RIO controller is placed between each sensor-actuator pair; and no direct communication between RIO controllers is assumed, leading to a set of decentralized controllers. To derive the condition for the natural mode entrainment, we use the multivariable harmonic balance (MHB) method with the describing function which approximates nonlinearities in the RIOs. Starting from one-DOF (degree of freedom) systems, we extend the analysis and synthesis methods to multi-DOF systems which have a special structure motivated by biological systems where actuators, sensors, stiffness and damping elements are all located at the same position. Due to the special structure, we can derive insightful information for the natural mode entrainment and develop a design method for the CPG-based decentralized controller. Furthermore, we extend the derived design method to general (non-collocated) systems with the aid of numerical computation. A positive rate feedback and negative integral feedback with saturation were found to be the fundamental mechanisms for the resonance entrainment of the one-DOF systems. However, the mechanisms are not sufficient for the multi-DOF systems, and an adaptation (or band-pass filtering) property is necessary for the natural mode entrainment. Although the design method is based on linear systems, the applicability to nonlinear systems is validated through numerical experiments.