Reid roundabout theorems for time scale symplectic systems

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Authors	ŠIMON HILSCHER Roman ZEIDAN Vera Michel
Year of publication	2010
Type	Article in Proceedings
Conference	Discrete Dynamics and Difference Equations
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.worldscibooks.com/mathematics/7470.html
Field	General mathematics
Keywords	Time scale; Riccati equation; Quadratic functional; Positivity; Nonnegativity; Normality; Controllability; Conjoined basis
Description	In this paper we survey Reid roundabout theorems for time scale symplectic systems (S). These theorems list equivalent conditions for the positivity and nonnegativity of the quadratic functional F associated with (S). The Reid roundabout theorems in this paper do not impose any normality assumption. We also show that Jacobi systems for nonlinear time scale control problems naturally lead to time scale symplectic systems, and that such a system consists of the Hamiltonian equations corresponding to the weak maximum principle for the quadratic functional F.
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