Asymptotic stabilization of passive systems without damping injection: A sampled integral-approximation technique

Passivity in physical systems is a restatement of energy balancing, therefore is an ubiquitous property in engineering applications. Under some weak conditions, the unique equilibrium state of a passive system is stable. However, to ensure asymptotic stability, strict passivity and a detectability property are required. Although strict 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-approximation stabilization (SIAS) technique for 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 SIAS is applicable to cascade connections of passive systems measuring only the storage function of the first subsystem and the output of the second one. Several examples, including a planar elbow manipulator and the controlled rigid body dynamics are shown to satisfy the required assumptions for the application of the SIAS.