论文信息 - Riccati inequality and other results for discrete symplectic systems

Riccati inequality and other results for discrete symplectic systems

In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals F associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of F with separated endpoints, (ii) a characterization of the nonnegativity of F for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of F with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems.

Roman Šimon Hilscher | R. Hilscher | Viera Růžičková | Viera Růžičková

[1] Vera Zeidan,et al. Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems , 2003 .

[2] T. Fortmann,et al. A matrix inversion identity , 1970 .

[3] Zur Positivität Diskreter Quadratischer Funktionale English Edition: on Positivity of Discrete Quadratic Functionals , 1995 .

[4] P. Řehák,et al. RICCATI INEQUALITY, DISCONJUGACY, AND RECIPROCITY PRINCIPLE FOR LINEAR HAMILTONIAN DYNAMIC SYSTEMS , 2003 .

[5] M. Bohner. Riccati Matrix Difference Equations and Linear Hamiltonian Difference Systems , 1996 .

[6] M. Bohner,et al. POSITIVE SEMIDEFINITENESS OF DISCRETE QUADRATIC FUNCTIONALS , 2003, Proceedings of the Edinburgh Mathematical Society.

[7] Martin Bohner,et al. An Oscillation Theorem for Discrete Eigenvalue Problems , 2003 .

[8] Martin Bohner,et al. Disconjugacy and Transformations for Symplectic Systems , 1997 .

[9] Symplectic Systems and Related Discrete Quadratic Functionals , 1997 .

[10] C. Ahlbrandt,et al. Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations , 1996 .

[11] Adi Ben-Israel,et al. Generalized inverses: theory and applications , 1974 .

[12] R. Hilscher. Reid Roundabout Theorem for Symplectic Dynamic Systems on Time Scales , 2001 .

[13] Vera Zeidan,et al. Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals , 2003 .