{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T07:13:29Z","timestamp":1780643609531,"version":"3.54.1"},"reference-count":37,"publisher":"SAGE Publications","issue":"8","license":[{"start":{"date-parts":[[2006,8,1]],"date-time":"2006-08-01T00:00:00Z","timestamp":1154390400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2006,8]]},"abstract":"<jats:p>Phase-Based Gain-Modulation (PBGM) control is realized by modulating controller gains in response to the phase of the system state or tracking error. PBGM controllers have been applied to robotic hands, parallel manipulators and flexible mechanisms to give increased damping, reduced tracking error and friction compensation.<\/jats:p>\n                  <jats:p>A novel method is presented to establish Lyapunov stability for PBGM control. Prior PBGM stability results incorporated a constraint which limited the range of provably stable systems. The present result removes this constraint, establishing Lyapunov stability for a substantially broader class of systems. Additionally, the new approach decouples the selection of the Lyapunov function from the controller design, permitting the controls designer to independently specify a switch function which determines the application of gain modulation.<\/jats:p>\n                  <jats:p>The present results are applied to analyze PBGM control of the Sarcos dextrous manipulator, illuminating the stability properties of control experiments previously reported in the literature. Numerical methods for design calculations are also presented.<\/jats:p>","DOI":"10.1177\/0278364906067543","type":"journal-article","created":{"date-parts":[[2006,7,12]],"date-time":"2006-07-12T06:37:30Z","timestamp":1152686250000},"page":"781-796","source":"Crossref","is-referenced-by-count":32,"title":["Stability of Phase-Based Gain Modulation with Designer-Chosen Switch Functions"],"prefix":"10.1177","volume":"25","author":[{"given":"Brian S. R.","family":"Armstrong","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Computer Science and Center for                         Industrial Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI                         53201-0784,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos\u00e9 A.","family":"Gutierrez","sequence":"additional","affiliation":[{"name":"Innovation Center, Eaton Corporation, 4201 N. 27 Street, Milwaukee, WI                         53216,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bruce A.","family":"Wade","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences and Center for Industrial                         Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413,"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ralph","family":"Joseph","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2006,8,1]]},"reference":[{"key":"atypb1","first-page":"478","volume-title":"Proceedings of IROS \u201897","author":"Armstrong, B."},{"issue":"2","key":"atypb2","first-page":"101","volume":"7","author":"Armstrong, B.","year":"1997","journal-title":"Applied Mathematics and Computer Science"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/87.911392"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1177\/02783640022067120"},{"key":"atypb5","volume-title":"Adaptive Control","author":"Astrom, K. J.","year":"1995"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574700003088"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-4563(199911)16:11<627::AID-ROB3>3.0.CO;2-B"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.809148"},{"key":"atypb9","volume-title":"Linear Systems","author":"DeCarlo, R. A.","year":"1989"},{"key":"atypb10","volume-title":"Practical Methods of Optimization","author":"Fletcher, R.","year":"1987","edition":"2"},{"key":"atypb11","unstructured":"Gutierrez, J. A. 2001. General stability of nonlinear PID control with                 arbitrary partial state knowledge. Master\u2019s thesis, University of                 Wisconsin, Milwaukee."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2004.11.013"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2005.863658"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2003.12.005"},{"key":"atypb15","volume-title":"16th IFAC World Congress (IFAC 2005)","author":"Heertjes, M. F."},{"key":"atypb16","first-page":"1794","volume-title":"Proceedings of 5th Euromech Nonlinear Dynamics Conference","author":"Heertjes, M. F."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(02)00139-5"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300402"},{"key":"atypb19","first-page":"516","volume-title":"Proceedings of 40th IEEE Conference on Decision and Control","author":"Jiang, F."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1080\/00207170412331330067"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/0957-4158(95)00080-1"},{"key":"atypb22","unstructured":"Kondriivtsev, L. 2002. NPID control with \u03b3-limiting and arbitrary                 partial-state knowledge. Master\u2019s thesis, University of Wisconsin, Milwaukee."},{"key":"atypb23","unstructured":"Kusik, T. P. 1999. Chatter in nonlinear proportional-integral-derivative                 (NPID) control, causes and remedies. Master\u2019s thesis, University of                 Wisconsin, Milwaukee."},{"key":"atypb24","volume-title":"Monte Carlo strategies in scientific computing","author":"Liu, J. S.","year":"2001"},{"key":"atypb25","unstructured":"Morse, R. A., Day, C. P., and Stoddard, K. A. 1988. Positional control method                 and system utilizing same, U.S. Patent 4,727,303."},{"key":"atypb26","first-page":"58","volume-title":"Proceedings of the 5th Asian Control Conference","author":"Peng, K."},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2004.06.002"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2005.854321"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1177\/027836499801700501"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1115\/1.2801198"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2004.824315"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cta:20030967"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2005.03.003"},{"key":"atypb34","first-page":"924","volume-title":"Proceedings of the 1994 International Conference on Robotics and Automation","author":"Xu, Y."},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1109\/37.341859"},{"key":"atypb36","first-page":"752","volume-title":"Proceedings of the 1993 International Conference on Robotics and Automation","author":"Xu, Y."},{"key":"atypb37","volume-title":"16th IFAC World Congress (IFAC 2005)","author":"Zheng, J."}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364906067543","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364906067543","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:15:49Z","timestamp":1777457749000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0278364906067543"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8]]},"references-count":37,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2006,8]]}},"alternative-id":["10.1177\/0278364906067543"],"URL":"https:\/\/doi.org\/10.1177\/0278364906067543","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,8]]}}}