{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,14]],"date-time":"2024-07-14T09:31:48Z","timestamp":1720949508249},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p> In this paper we prove the general result that, given a linear system [Formula: see text] where A is hyperbolic, u is piecewise linear and L-periodic, with [Formula: see text], then there exists a unique L-periodic solution x = x<jats:sub>p<\/jats:sub>(t) such that [Formula: see text]. We then consider a DC\/DC buck (step-down) converter controlled by the ZAD (zero-average dynamics) strategy. The ZAD strategy sets the duty cycle, d (the length of time the input voltage is applied across an inductance), by ensuring that, on average, a function of the state variables is always zero. The two control parameters are v<jats:sub> ref <\/jats:sub>, a reference voltage that the circuit is required to follow, and k<jats:sub>s<\/jats:sub>, a time constant which controls the approach to the zero average. We show how to calculate d exactly for a periodic system response, without knowledge of the state space solutions. In particular, we show that for a T-periodic response d is independent of k<jats:sub>s<\/jats:sub>. We calculate period doubling and corner collision bifurcations, the latter occurring when the duty cycle saturates and is unable to switch. We also show the presence of a codimension two nonsmooth bifurcation in this system when a corner collision bifurcation and a saddle node bifurcation collide. <\/jats:p>","DOI":"10.1142\/s0218127409022907","type":"journal-article","created":{"date-parts":[[2009,3,20]],"date-time":"2009-03-20T06:36:08Z","timestamp":1237530968000},"page":"349-357","source":"Crossref","is-referenced-by-count":10,"title":["TWO-PARAMETER BIFURCATION CURVES IN POWER ELECTRONIC CONVERTERS"],"prefix":"10.1142","volume":"19","author":[{"given":"E.","family":"FOSSAS","sequence":"first","affiliation":[{"name":"Institute of Industrial and Control Engineering, Universitat Polit\u00e8cnica de Catalunya, Av. Diagonal 647, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. J.","family":"HOGAN","sequence":"additional","affiliation":[{"name":"Department of Engineering Mathematics, Queen's Building, University Walk, Bristol BS8 1TR, England"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. M.","family":"SEARA","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics I, Universitat Polit\u00e8cnica de Catalunya, Av. Diagonal 647, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405014015"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/9780470545393"},{"key":"rf5","unstructured":"D.\u00a0Biel, E.\u00a0Fossas and R.\u00a0Gri\u00f1\u00f3, Advances in Variable Structure System, Analysis, Integration and Applications, eds. X.\u00a0Yu and J.X.\u00a0Xu (World Scientific, Singapore, 2001)\u00a0pp. 335\u2013344."},{"key":"rf8","volume-title":"Bifurcations in Piecewise-Smooth Dynamical Systems: Theory and Applications","author":"Di Bernardo M.","year":"2007"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/81.481457"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015015"},{"key":"rf12","volume-title":"Power Electronics: Converters, Applications, and Design","author":"Mohan N.","year":"2002"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1109\/TPEL.2002.807164"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1109\/81.703837"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409022907","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:03:26Z","timestamp":1565121806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409022907"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1142\/S0218127409022907"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409022907","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}