Riccati equations for abnormal time scale quadratic functionals

• 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: HILSCHER, Roman and Vera Michel ZEIDAN. Riccati equations for abnormal time scale quadratic functionals. Journal of Differential Equations. San Diego (USA): Elsevier Science, 2008, vol. 244, No 6, p. 1410-1447. ISSN 0022-0396.
• 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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