LEADER 05021nam 22007335 450 001 9910254061703321 005 20220330171746.0 010 $a3-319-29025-8 024 7 $a10.1007/978-3-319-29025-6 035 $a(CKB)3710000000621633 035 $a(EBL)4459491 035 $a(SSID)ssj0001654112 035 $a(PQKBManifestationID)16432923 035 $a(PQKBTitleCode)TC0001654112 035 $a(PQKBWorkID)14982864 035 $a(PQKB)10071957 035 $a(DE-He213)978-3-319-29025-6 035 $a(MiAaPQ)EBC4459491 035 $a(PPN)192772171 035 $a(EXLCZ)993710000000621633 100 $a20160325d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNonautonomous linear Hamiltonian systems: oscillation, spectral theory and control /$fby Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (515 p.) 225 1 $aDevelopments in Mathematics,$x1389-2177 ;$v36 300 $aDescription based upon print version of record. 311 $a3-319-29023-1 320 $aIncludes bibliographical references and index. 327 $aNonautonomous linear Hamiltonian systems -- The rotation number and the Lyapunov index for real nonautonomous linear Hamiltonian systems -- The Floquet coeffcient for nonautonomous linear Hamiltonian systems: Atkinson problems -- The Weyl functions -- Weak disconjugacy for linear Hamiltonian systems -- Nonautonomous control theory. Linear regulator problem and the Kalman-Bucy filter -- Nonautonomous control theory. A general version of the Yakubovich Frequency Theorem -- Nonautonomous control theory. Linear-quadratic dissipative control processes -- Index -- References. 330 $aThis monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory. 410 0$aDevelopments in Mathematics,$x1389-2177 ;$v36 606 $aDynamics 606 $aErgodic theory 606 $aDifferential equations 606 $aSystem theory 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aDifferential equations. 615 0$aSystem theory. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aOrdinary Differential Equations. 615 24$aSystems Theory, Control. 676 $a510 700 $aJohnson$b Russell$4aut$4http://id.loc.gov/vocabulary/relators/aut$0799413 702 $aObaya$b Rafael$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aNovo$b Sylvia$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aNúñez$b Carmen$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aFabbri$b Roberta$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254061703321 996 $aNonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control$92124853 997 $aUNINA