{"ID":2822804,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.01385","arxiv_id":"2601.01385","title":"On IDA-PBC with Maximum Energy Shapeability","abstract":"Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a well-established stabilization technique for affine nonlinear systems. However, its application is generally hindered by the requirement of solving a set of partial differential equations (PDEs), i.e., the so-called matching equation. This paper introduces the notion of \\emph{maximum energy shapeability} which describes the scenario that the homogeneous part of the matching equation admits $m$ independent solutions with $m$ the dimension of the control input. We demonstrate that the maximum energy shapeability enables a systematic procedure for the IDA-PBC design by transforming the matching equation into a set of easier-to-solve PDEs. Sufficient conditions for maximum energy shapeability are also provided. It is shown that some existing constructive IDA-PBC designs actually implicitly exploit the maximum energy shapeability. The proposed procedure for the IDA-PBC design is illustrated with the magnetic levitation system.","short_abstract":"Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a well-established stabilization technique for affine nonlinear systems. However, its application is generally hindered by the requirement of solving a set of partial differential equations (PDEs), i.e., the so-called matching equation. This pa...","url_abs":"https://arxiv.org/abs/2601.01385","url_pdf":"https://arxiv.org/pdf/2601.01385v1","authors":"[\"Ziheng Jiao\",\"Chengshuai Wu\",\"Bo Fan\",\"Meng Zhang\",\"Romeo Ortega\"]","published":"2026-01-04T05:40:29Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.DS\"]","methods":"[]","has_code":false}