HILSCHER, Roman. Comparison results for solutions of time scale matrix Riccati equations and inequalities. The Australian Journal of Mathematical Analysis and Applications. Victoria, Austrálie: Australian Internet Publishing, 2006, vol. 3, No 2, p. Article 13, 1-15, 15 pp. ISSN 1449-5910.
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Basic information
Original name Comparison results for solutions of time scale matrix Riccati equations and inequalities
Name in Czech Srovnávací kritéria pro řešení maticových Riccatiho rovnic a nerovnic na time scales
Authors HILSCHER, Roman (203 Czech Republic, guarantor).
Edition The Australian Journal of Mathematical Analysis and Applications, Victoria, Austrálie, Australian Internet Publishing, 2006, 1449-5910.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Australia
Confidentiality degree is not subject to a state or trade secret
RIV identification code RIV/00216224:14310/06:00015472
Organization unit Faculty of Science
Keywords in English Time scale; Time scale symplectic system; Linear Hamiltonian system; Matrix Riccati equation; Riccati inequality; Conjoined basis
Tags conjoined basis, Linear hamiltonian system, Matrix Riccati equation, Riccati inequality, time scale, Time scale symplectic system
Tags International impact, Reviewed
Changed by Changed by: prof. RNDr. Roman Šimon Hilscher, DSc., učo 1023. Changed: 4/12/2006 11:31.
Abstract
In this paper we derive comparison results for Hermitian solutions of time scale matrix Riccati equations and Riccati inequalities. Such solutions arise from special conjoined bases (X,U) of the corresponding time scale symplectic system via the Riccati quotient Q=UX-1. We also discuss properties of a unitary matrix solution \hat Q=(U+iX)(U-iX)-1 of a certain associated Riccati equation.
Abstract (in Czech)
V tomto článku jsme odvodili srovnávací kritéria pro Hermiteovská řešení maticových Riccatiho rovnic a nerovnic na time scales. Taková řešení vznikají ze speciálních izotropických bází (X,U) příslušného symplektického systému na time scales pomocí Riccatiho podílu Q=UX-1. Také dále studujeme vlastnosti unitárních maticových řešení \hat Q=(U+iX)(U-iX)-1 jisté přidružené Riccatiho rovnice.
Links
GA201/04/0580, research and development projectName: Diferenční rovnice a dynamické rovnice na "time scales"
Investor: Czech Science Foundation, Difference Equations and Dynamic Equations on Time Scales.
KJB1019407, research and development projectName: Lineární Hamiltonovské dynamické systémy a pololineární dynamické rovnice
Investor: Academy of Sciences of the Czech Republic, Linear Hamiltonian dynamic systems and half-linear dynamic equations
1K04001, research and development projectName: Podmínky optimality na "time scales"
Investor: Ministry of Education, Youth and Sports of the CR, Optimality conditions on time scales
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