Inequalities and Asymptotics for Riccati Matrix Difference Operators

Journal of Mathematical Analysis and Applications

Volumn 221, Issue 1, 1998, Pages 262-286

  Bohner, Martin ^a   Došlý, Ondřej ^b   Kratz, Werner ^c  

^a SAN DIEGO STATE UNIVERSITY   (United States)

^b MASARYK UNIVERSITY   (Czech Republic)

^c UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039494918     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5890     Document Type: Article

References (25)

1. Agarwal R. Difference Equations and Inequalities. 1992;Dekker, New York.
2. Ahlbrandt C. D. Continued fraction representations of maximal and minimal solutions of a discrete matrix Riccati equation. SIAM J. Math. Anal. 24:1993;1597-1621.
3. C. D. Ahlbrandt, M. Heifetz, Discrete Riccati equations of filtering and control, in, Conference Proceedings of the First International Conference on Difference Equations, San Antonio, 1994, 1, 16, Gordon & Breach, New York, 1994.
4. Ahlbrandt C. D., Hooker J. W. Recessive solutions of symmetric three term recurrence relations. Canad. Math. Soc. Conf. Proc. 8:1987;3-42.
5. Ahlbrandt C. D., Peterson A. C. Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations. 1996;Kluwer Academic, Boston.
6. M. Bohner, Zur Positivität diskreter quadratischer Funktionale, Universität Ulm, 1995.
7. Bohner M. Linear Hamiltonian difference systems: Disconjugacy and Jacobi type conditions. J. Math. Anal. Appl. 199:1996;804-826.
8. Bohner M. On disconjugacy for Sturm-Liouville difference equations. J. Difference Equations. 2:1996;227-237.
9. Bohner M. Riccati matrix difference equations and linear Hamiltonian difference systems. Dynamics Continuous Discrete Impulsive Systems. 2:1996;147-159.
10. M. Bohner, Discrete linear Hamiltonian eigenvalue problems, Comput. Math. Appl.
11. Bohner M., Došly O. Disconjugacy and transformations for symplectic systems. Rocky Mountain J. Math. 27:1997;707-743.
12. Erbe L., Yan P. Disconjugacy for linear Hamiltonian difference systems. J. Math. Anal. Appl. 167:1992;355-367.
13. Erbe L., Yan P. Qualitative properties of Hamiltonian difference systems. J. Math. Anal. Appl. 171:1992;334-345.
14. Erbe L., Yan P. Oscillation criteria for Hamiltonian matrix difference systems. Proc. Amer. Math. Soc. 119:1993;525-533.
15. Erbe L., Yan P. On the discrete Riccati equation and its applications to discrete Hamiltonian systems. Rocky Mountain J. Math. 25:1995;167-178.
16. Hartman P. Difference equations: disconjugacy, principal solutions, Green's functions, complete monotonicity. Trans. Amer. Math. Soc. 246:1978;1-30.
17. Kratz W. A substitute of l'Hospital's rule for matrices. Proc. Amer. Math. Soc. 99:1987;395-402.
18. Kratz W. On the optimal linear regulator. Internat. J. Control. 60:1994;1005-1013.
19. W. Kratz, An inequality for finite differences via asymptotics of Riccati matrix difference equations, J. Difference Equations.
20. Kratz W. Quadratic Functionals in Variational Analysis and Control Theory. 1995;Akademie Verlag, Berlin.
21. Rau A. C. M., Vreudgenhil R. Existence and comparison theorems for algebraic Riccati equations for continuous and discrete-time systems. Linear Algebra Appl. 99:1988;63-83.
22. Reid W. T. Ordinary Differential Equations. 1971;Wiley, New York.
23. Reid W. T. Sturmian Theory for Ordinary Differential Equations. 1980;Springer-Verlag, New York.
24. Riordan J. Combinatorial Identities. 1968;Wiley, New York.
25. Sturm C. Sur les équations différentielles linéaires du second order. J. Math. Pures Appl. 1:1836;106-186.