Riccati equations for abnormal time scale quadratic functionals

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Authors	HILSCHER Roman ZEIDAN Vera Michel
Year of publication	2008
Type	Article in Periodical
Magazine / Source	Journal of Differential Equations
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJ2-4R3BWJF-5&_user=835458&_coverDate=03%2F15%2F2008&_alid=691313609&_rdoc=1&_fmt=summary&_orig=search&_cdi=6866&_sort=d&_docanchor=&view=c&_ct=2&_acct=C000045159&_version=1&_urlVersion=0&_userid
Field	General mathematics
Keywords	Time scale; Riccati equation; Quadratic functional; Positivity; Nonnegativity; Normality; Controllability; Conjoined basis
Description	This paper focuses on developing new Riccati-type conditions for an abnormal time scale symplectic system (S). These conditions provide characterizations of the nonnegativity (with and without a certain ``image condition'') and positivity of the quadratic functionals associated with such a system. The novelty of these conditions rely on the natural conjoined basis (X_a,U_a) of (S) in which X_a(t) is not necessarily invertible, and thus the system (S) could be abnormal. These results are new even in the special case of continuous time, as are some of them in the discrete time setting.
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