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polderman j introduction mathematical systems theory 1998

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Textbook in PDF and DJVU formats Preface How to Use tbis Book Dynamical Systems Introduction Models The universum and the behavior Behavioral equations Latent variables Dynamical Systems The basic concept Latent variables in dynamical systems Linearity and Time-Invariance Dynamical Behavioral Equations Recapitulation Notes and References Exercises Systems Defined by Linear Differential Equations Introduction Notation Constant-Coefficient Differential Equations Linear constant-coefficient differential equations Weak solutions of differential equations Behaviors Defined by Differential Equations Topological properties of the behavior Linearity and time-invariance The Calculus of Equations Polynomial rings and polynomial matrices Equivalent representations Elementary row operations and unimodular polynomial matrices The Bezout identity Left and right unimodular transformations Minimal and full row rank representations Recapitulation Notes and References Exercises Analytical problems Algebraic problems Time Domain Description of Linear Systems Introduction Autonomous Systems The scalar case The multivariable case Systems in Input/Output Form Systems Defined by an Input/Output Map Relation Between Differential Systems and Convolution Systems When Are Two Representations Equivalent? Recapitulation Notes and References Exercises State Space Models Introduction Differential Systems with Latent Variables State Space Models Input/State/Output Models The Behavior of i/s/o Models The zero input case The nonzero input case: The variation of the constants formula The input/state/output behavior How to calculate e^{At}? Via the Jordan form Using the theory of autonomous behaviors Using the partial fraction expansion of (l-A)^{-} State Space Transformations Linearization of Nonlinear i/s/o Systems Recapitulation Notes and References Exercises Controllability and Observability Introduction Controllability Controllability of input/state/output systems Controllability of i/s systems Controllability of i/s/o systems Stabilizability Observability Observability of i/s/o systems Detectability The Kalman Decomposition Polynomial Tests for Controllability and Observability Recapitulation Notes and References Exercises Elimination of Latent Variables and State Space Representations Introduction Elimination of Latent Variables Modeling from first principles Elimination procedure Elimination of latent variables in interconnections Elimination of State Variables From i/o to i/s/o Model The observer canonical form The controller canonical form Canonical Forms and Minimal State Space Representations Canonical forms Equivalent state representations Minimal state space representations Image Representations Recapitulation Notes and References Exercises Stability Theory Introduction Stability of Autonomous Systems The Routh-Hurwitz Conditions The Routh test The Hurwitz test The Lyapunov Equation Stability by Linearization Input/Output Stability Recapitulation Notes and References Exercises Time- and Frequency-Domain Characteristics of Linear Time-Invariant Systems Introduction The Transfer Function and the Frequency Response Convolution systems Differential systems The transfer function represents the controllable part of the behavior The transfer function of interconnected systems Time-Domain Characteristics Frequency-Domain Response Characteristics The Bode plot The Nyquist plot First- and Second-Order Systems First-order systems Second-order systems Rational Transfer Functions Pole/zero diagram The transfer function of i/s/o representations The Bode plot of rational transfer functions Recapitulation Notes and References Exercises Pole Placement by State Feedback Open Loop and Feedback Control Linear State Feedback The Pole Placement Problem Proof of the Pole Placement Theorem System similarity and pole placement Controllability is necessary for pole placement Pole placement for controllable single-input systems Pole placement for controllable multi-input systems Algorithms for Pole Placement Stabilization Stabiization of Nonlinear Systems Recapitulation Notes and References Exercises Observers and Dynamic Compensators Introduction State Observers Pole Placement in Observers Unobservable Systems Feedback Compensators Reduced Order Observers and Compensators Stabilization of Nonlinear Systems Control in a Behavioral Setting Motivation Control as interconnection Pole placement An algorithm for pole placement Recapitulation Notes and References Exercises Simulation Exercises Stabilization of a Cart Temperature Control of a Container Autonomous Dynamics of Coupled Masses Satellite Dynamics Motivation Mathematical modeing Equilibrium Analysis Linearization Analysis of the model Simulation Dynamics of a Motorbike Stabilization of a Double Pendulum Modeling Linearization Analysis Stabilization Notes and References Background Material Polynomial Matrices Partial Fraction Expansion Fourier and Laplace Transforms Fourier transform Laplace transform Notes and References Exercises Notation References Index

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polderman j introduction mathematical systems theory 1998