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. © 2010 Elsevier Ltd. All rights reserved.