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Linear systems / / Gordon Blower
Linear systems / / Gordon Blower
Autore Blower G (Gordon)
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer International Publishing, , [2023]
Descrizione fisica 1 online resource (417 pages)
Disciplina 629.8
Collana Mathematical Engineering
Soggetto topico Automatic control
Automatic control - Data processing
ISBN 9783031212406
9783031212390
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- 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.
5.5 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.
8.5 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.
Record Nr. UNINA-9910644265903321
Blower G (Gordon)  
Cham, Switzerland : , : Springer International Publishing, , [2023]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Linear systems / / Gordon Blower
Linear systems / / Gordon Blower
Autore Blower G (Gordon)
Edizione [1st ed. 2022.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer International Publishing, , [2023]
Descrizione fisica 1 online resource (417 pages)
Disciplina 629.8
Collana Mathematical Engineering
Soggetto topico Automatic control
Automatic control - Data processing
Sistemes lineals
Soggetto genere / forma Llibres electrònics
ISBN 9783031212406
9783031212390
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- 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.
5.5 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.
8.5 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.
Record Nr. UNISA-996508571903316
Blower G (Gordon)  
Cham, Switzerland : , : Springer International Publishing, , [2023]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui