LEADER 01610nam 2200325Ia 450 001 996397453503316 005 20200824132441.0 035 $a(CKB)4940000000061438 035 $a(EEBO)2240889664 035 $a(OCoLC)ocm31355250e 035 $a(OCoLC)31355250 035 $a(EXLCZ)994940000000061438 100 $a19941025d1695 uy | 101 0 $aeng 135 $aurbn||||a|bb| 200 12$aA form of prayer and thanksgiving to almighty God$b[electronic resource] $eto be used throughout the cities of London and Westminster, and elsewhere within the weekly bills of mortality, on Sunday the eighth day of this instant September, and in all other places throughout the kingdom of England, dominion of Wales, and town of Berwick upon Tweed, on Sunday the twenty second day of the same month, for granting to the forces of His Majesty, and his allies so great success in the taking the town of Namur, and for protecting His Majesties sacred person from the many dangers to which he was so frequently exposed during that siege 210 $aLondon $cPrinted by Charles Bill, and the executrix of Thomas Newcomb, deceas'd ...$dM DC XCV [1695] 215 $a[19] p 300 $aImperfect: print show-through, with loss of text. 300 $a"By order of the lords justices." 300 $aReproduction of original in Harvard University Library. 330 $aeebo-0062 606 $aPrayers 615 0$aPrayers. 801 2$bUMI 801 2$bWaOLN 906 $aBOOK 912 $a996397453503316 996 $aA form of prayer and thanksgiving to Almighty God$92309996 997 $aUNISA LEADER 08232nam 2200553 450 001 996508571903316 005 20231005194608.0 010 $a9783031212406$b(electronic bk.) 010 $z9783031212390 024 7 $a10.1007/978-3-031-21240-6 035 $a(MiAaPQ)EBC7176393 035 $a(Au-PeEL)EBL7176393 035 $a(CKB)25997731400041 035 $a(DE-He213)978-3-031-21240-6 035 $a(PPN)267808259 035 $a(EXLCZ)9925997731400041 100 $a20230503d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLinear systems /$fGordon Blower 205 $a1st ed. 2022. 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2023] 210 4$d©2023 215 $a1 online resource (417 pages) 225 1 $aMathematical Engineering,$x2192-4740 311 08$aPrint version: Blower, Gordon Linear Systems Cham : Springer International Publishing AG,c2023 9783031212390 327 $aIntro -- Preface -- Contents -- 1 Linear Systems and Their Description -- 1.1 Linear Systems and Their Description -- 1.2 Feedback -- 1.3 Linear Differential Equations -- 1.4 Damped Harmonic Oscillator -- 1.5 Reduction of Order of Linear ODE -- 1.6 Exercises -- 2 Solving Linear Systems by Matrix Theory -- 2.1 Matrix Terminology -- 2.2 Characteristic Polynomial -- 2.3 Norm of a Vector -- 2.4 Cauchy-Schwarz Inequality -- 2.5 Matrix Exponential exp(A) or expm (A) -- 2.6 Exponential of a Diagonable Matrix -- 2.7 Solving MIMO (A,B,C,D) -- 2.8 Rational Functions -- 2.9 Block Matrices -- 2.10 The Transfer Function of (A,B,C,D) -- 2.11 Realization with a SISO -- 2.12 Exercises -- 3 Eigenvalues and Block Decompositions of Matrices -- 3.1 The Transfer Function of Similar SISOs (A,B,C,D) -- 3.2 Jordan Blocks -- 3.3 Exponentials and Eigenvalues of Complex Matrices -- 3.4 Exponentials and the Resolvent -- 3.5 Schur Complements -- 3.6 Self-adjoint Matrices -- 3.7 Positive Definite Matrices -- 3.8 Linear Fractional Transformations -- 3.9 Stable Matrices -- 3.10 Dissipative Matrices -- 3.11 A Determinant Formula -- 3.12 Observability and Controllability -- 3.13 Kalman's Decomposition -- 3.14 Kronecker Product of Matrices -- 3.15 Exercises -- 4 Laplace Transforms -- 4.1 Laplace Transforms -- 4.2 Laplace Convolution -- 4.3 Laplace Uniqueness Theorem -- 4.4 Laplace Transform of a Differential Equation -- 4.5 Solving MIMO by Laplace Transforms -- 4.6 Partial Fractions -- 4.7 Dirichlet's Integral and Heaviside's Expansions -- 4.8 Final Value Theorem -- 4.9 Laplace Transforms of Periodic Functions -- 4.10 Fourier Cosine Transform -- 4.11 Impulse Response -- 4.12 Transmitting Signals -- 4.13 Exercises -- 5 Transfer Functions, Frequency Response, Realization and Stability -- 5.1 Winding Numbers -- 5.2 Realization -- 5.3 Frequency Response -- 5.4 Nyquist's Locus. 327 $a5.5 Gain and Phase -- 5.6 BIBO Stability -- 5.7 Undamped Harmonic Oscillator: Marginal Stability and Resonance -- 5.8 BIBO Stability in Terms of Eigenvalues of A -- 5.9 Maxwell's Stability Problem -- 5.10 Stable Rational Transfer Functions -- 5.11 Nyquist's Criterion for Stability of T -- 5.12 Nyquist's Criterion Proof -- 5.13 M and N Circles -- 5.14 Exercises -- 6 Algebraic Characterizations of Stability -- 6.1 Feedback Control -- 6.2 PID Controllers -- 6.3 Stable Cubics -- 6.4 Hurwitz's Stability Criterion -- 6.5 Units and Factors -- 6.6 Euclidean Algorithm and Principal Ideal Domains -- 6.7 Ideals in the Complex Polynomials -- 6.8 Highest Common Factor and Common Zeros -- 6.9 Rings of Fractions -- 6.10 Coprime Factorization in the Stable Rational Functions -- 6.11 Controlling Rational Systems -- 6.12 Invariant Factors -- 6.13 Matrix Factorizations to Stabilize MIMO -- 6.14 Inverse Laplace Transforms of Strictly Proper Rational Functions -- 6.15 Differential Rings -- 6.16 Bessel Functions of Integral Order -- 6.17 Exercises -- 7 Stability and Transfer Functions via Linear Algebra -- 7.1 Lyapunov's Criterion -- 7.2 Sylvester's Equation AY+YB+C=0 -- 7.3 A Solution of Lyapunov's Equation AL+LA' +P=0 -- 7.4 Stable and Dissipative Linear Systems -- 7.5 Almost Stable Linear Systems -- 7.6 Simultaneous Diagonalization -- 7.7 A Linear Matrix Inequality -- 7.8 Differential Equations Relating to Sylvester's Equation -- 7.9 Transfer Functions tf -- 7.10 Small Groups of Matrices -- 7.11 How to Convert Complex Matrices into Real Matrices -- 7.12 Periods -- 7.13 Discrete Fourier Transform -- 7.14 Exercises -- 8 Discrete Time Systems -- 8.1 Discrete-Time Linear Systems -- 8.2 Transfer Function for a Discrete Time Linear System -- 8.3 Correspondence Between Continuous- and Discrete-Time Systems -- 8.4 Chebyshev Polynomials and Filters. 327 $a8.5 Hankel Matrices and Moments -- 8.6 Orthogonal Polynomials -- 8.7 Hankel Determinants -- 8.8 Laguerre Polynomials -- 8.9 Three-Term Recurrence Relation -- 8.10 Moments via Discrete Time Linear Systems -- 8.11 Floquet Multipliers -- 8.12 Exercises -- 9 Random Linear Systems and Green's Functions -- 9.1 ARMA Process -- 9.2 Distributions on a Bounded Interval -- 9.3 Cauchy Transforms -- 9.4 Herglotz Functions -- 9.5 Green's Functions -- 9.6 Random Diagonal Transformations -- 9.7 Wigner Matrices -- 9.8 Pastur's Theorem -- 9.9 May-Wigner Model -- 9.10 Semicircle Addition Law -- 9.11 Matrix Version of Pastur's Fixed Point Equation -- 9.12 Rank One Perturbations on Green's Functions -- 9.13 Exercises -- 10 Hilbert Spaces -- 10.1 Hilbert Sequence Space -- 10.2 Hardy Space on the Disc -- 10.3 Subspaces and Blocks -- 10.4 Shifts and Multiplication Operators -- 10.5 Canonical Model -- 10.6 Hardy Space on the Right Half-Plane -- 10.7 Paley-Wiener Theorem -- 10.8 Rational Filters -- 10.9 Shifts on L2 -- 10.10 The Telegraph Equation as a Linear System -- 10.11 Exercises -- 11 Wireless Transmission and Wavelets -- 11.1 Frequency Band Limited Functions and Sampling -- 11.2 The Shannon Wavelet -- 11.3 Telatar's Model of Wireless Communication -- 11.4 Exercises -- 12 Solutions to Selected Exercises -- Glossary of Linear Systems Terminology -- A MATLAB Commands for Matrices -- B SciLab Matrix Operations -- References -- Index. 330 $aThis textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing. The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis. The book mainly covers linear systems with finite-dimensional state spaces. Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB. Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail. The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatar?s model for multiple antenna transmission. One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system. The final chapter covers modern applications to signal processing, Whittaker?s sampling theorem for band-limited functions, and Shannon?s wavelet. Based on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering. The prerequisites are basic linear algebra and complex analysis. 410 0$aMathematical Engineering,$x2192-4740 606 $aAutomatic control 606 $aAutomatic control$xData processing 606 $aSistemes lineals$2thub 608 $aLlibres electrònics$2thub 615 0$aAutomatic control. 615 0$aAutomatic control$xData processing. 615 7$aSistemes lineals 676 $a629.8 700 $aBlower$b G$g(Gordon),$0321964 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a996508571903316 996 $aLinear Systems$93004758 997 $aUNISA LEADER 00899nam0 22002411i 450 001 UON00197540 005 20231205103239.582 100 $a20030730d1973 |0itac50 ba 101 $aita 102 $aIT 105 $a|||| ||||| 200 1 $aControrivoluzione e rivolta$fHerbert Marcuse 210 $a[Milano] Arnaldo Mondadori Editore$d1973 215 $a178 p.$d23 cm. - 316 $aAME VI c 8 0493$5IT-UONSI AMEVI c8/SMARRITO 700 1$aMarcuse$bHerbert$3UONV103336$032576 712 $aMondadori$3UONV245964$4650 801 $aIT$bSOL$c20250808$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00197540 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI VI c 8 SMARRITO $eSI SI 8166 6 SMARRITO AME VI c 8 0493$sSmarrito 996 $aControrivoluzione e rivolta$994433 997 $aUNIOR