Optimal control approach to stability criteria on Hill's equations

(整期优先)网络出版时间:2018-03-13
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ThispapergivesatutorialonhowtoproveLyapunovtypecriteriabyoptimalcontrolmethods.Firstly,weconsiderstabilitycriteriaonHill'sequationswithnonnegativepotential.Byoptimalcontrolmethodsdevelopedin1990s,weobtainseveralstabilitycriteriaincludingLyapunov'scriterion,Ne..gauzandLidski'scriterion.Secondly,wepresentstabilitycriteriaonHill'sequationswithsign-changingpotentialinwhichBrog'scriterionandKrein'scriterionareincluded.