Asymptotic stabilization of passive systems without damping injection: a sampled integral technique

Passivity in physical systems is a restatement of energy balancing, and therefore is a ubiquitous property in engineering applications. Under some weak conditions, the unique equilibrium state of passive systems is stable. However, to ensure asymptotic stability, strict output passivity and a detectability property are required. Although strict output passivity may be enforced via a damping injection that feeds back the passive output, this signal may be noisy or unmeasurable — the paradigmatic example being velocity in mechanical systems. In this paper a sampled integral stabilization (SIS) technique for the asymptotic regulation of passive systems, that requires only the knowledge of the time integral of the passive output — i.e. position in mechanical systems — is proposed. As a generalization of the previous result, it is shown that SIS is applicable to cascade connections of passive systems measuring only the storage function of the second one. Several examples, including a planar elbow manipulator and the rigid body dynamics are shown to satisfy the assumptions for the application of SIS.