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@article{759057, author = {Hilscher, Roman and Zeidan, Vera Michel}, article_location = {San Diego (USA)}, article_number = {6}, keywords = {Time scale; Riccati equation; Quadratic functional; Positivity; Nonnegativity; Normality; Controllability; Conjoined basis}, language = {eng}, issn = {0022-0396}, journal = {Journal of Differential Equations}, title = {Riccati equations for abnormal time scale quadratic functionals}, url = {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}, volume = {244}, year = {2008} }
TY - JOUR ID - 759057 AU - Hilscher, Roman - Zeidan, Vera Michel PY - 2008 TI - Riccati equations for abnormal time scale quadratic functionals JF - Journal of Differential Equations VL - 244 IS - 6 SP - 1410-1447 EP - 1410-1447 PB - Elsevier Science SN - 00220396 KW - Time scale KW - Riccati equation KW - Quadratic functional KW - Positivity KW - Nonnegativity KW - Normality KW - Controllability KW - Conjoined basis UR - 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 N2 - 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 (Xa,Ua) of (S) in which Xa(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. ER -
HILSCHER, Roman a Vera Michel ZEIDAN. Riccati equations for abnormal time scale quadratic functionals. \textit{Journal of Differential Equations}. San Diego (USA): Elsevier Science, 2008, roč.~244, č.~6, s.~1410-1447. ISSN~0022-0396.
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