Cover -- Title -- Copyright -- Dedication -- CONTENTS -- PREAMBLE -- LINEAR SYSTEMS I — BASIC CONCEPTS -- I SYSTEM REPRESENTATION -- 1 STATE-SPACE LINEAR SYSTEMS -- 1.1 State-Space Linear Systems -- 1.2 Block Diagrams -- 1.3 Exercises -- 2 LINEARIZATION -- 2.1 State-Space Nonlinear Systems -- 2.2 Local Linearization Around an Equilibrium Point -- 2.3 Local Linearization Around a Trajectory -- 2.4 Feedback Linearization -- 2.5 Practice Exercises -- 2.6 Exercises -- 3 CAUSALITY, TIME INVARIANCE, AND LINEARITY -- 3.1 Basic Properties of LTV/LTI Systems -- 3.2 Characterization of All Outputs to a Given Input -- 3.3 Impulse Response -- 3.4 Laplace and Ƶ Transforms (Review) -- 3.5 Transfer Function -- 3.6 Discrete-Time Case -- 3.7 Additional Notes -- 3.8 Exercises -- 4 IMPULSE RESPONSE AND TRANSFER FUNCTION OF STATE-SPACE SYSTEMS -- 4.1 Impulse Response and Transfer Function for LTI Systems -- 4.2 Discrete-Time Case -- 4.3 Elementary Realization Theory -- 4.4 Equivalent State-Space Systems -- 4.5 LTI Systems in MATLAB® -- 4.6 Practice Exercises -- 4.7 Exercises -- 5 SOLUTIONS TO LTV SYSTEMS -- 5.1 Solution to Homogeneous Linear Systems -- 5.2 Solution to Nonhomogeneous Linear Systems -- 5.3 Discrete-Time Case -- 5.4 Practice Exercises -- 5.5 Exercises -- 6 SOLUTIONS TO LTI SYSTEMS -- 6.1 Matrix Exponential -- 6.2 Properties of the Matrix Exponential -- 6.3 Computation of Matrix Exponentials Using Laplace Transforms -- 6.4 The Importance of the Characteristic Polynomial -- 6.5 Discrete-Time Case -- 6.6 Symbolic Computations in MATLAB® -- 6.7 Practice Exercises -- 6.8 Exercises -- 7 SOLUTIONS TO LTI SYSTEMS: THE JORDAN NORMAL FORM -- 7.1 Jordan Normal Form -- 7.2 Computation of Matrix Powers using the Jordan Normal Form -- 7.3 Computation of Matrix Exponentials using the Jordan Normal Form -- 7.4 Eigenvalues with Multiplicity Larger than 1 -- 7.5 Practice Exercise -- 7.6 Exercises -- II STABILITY -- 8 INTERNAL OR LYAPUNOV STABILITY -- 8.1 Lyapunov Stability -- 8.2 Vector and Matrix Norms (Review) -- 8.3 Eigenvalue Conditions for Lyapunov Stability -- 8.4 Positive-Definite Matrices (Review) -- 8.5 Lyapunov Stability Theorem -- 8.6 Discrete-Time Case -- 8.7 Stability of Locally Linearized Systems -- 8.8 Stability Tests with MATLAB® -- 8.9 Practice Exercises -- 8.10 Exercises -- 9 INPUT-OUTPUT STABILITY -- 9.1 Bounded-Input, Bounded-Output Stability -- 9.2 Time Domain Conditions for BIBO Stability -- 9.3 Frequency Domain Conditions for BIBO Stability -- 9.4 BIBO versus Lyapunov Stability -- 9.5 Discrete-Time Case -- 9.6 Practice Exercises -- 9.7 Exercises -- 10 PREVIEW OF OPTIMAL CONTROL -- 10.1 The Linear Quadratic Regulator Problem -- 10.2 Feedback Invariants -- 10.3 Feedback Invariants in Optimal Control -- 10.4 Optimal State Feedback -- 10.5 LQR with MATLAB® -- 10.6 Practice Exercise -- 10.7 Exercise -- III CONTROLLABILITY AND STATE FEEDBACK -- 11 CONTROLLABLE AND REACHABLE SUBSPACES -- 11.1 Controllable and Reachable Subspaces -- 11.2 Physical Examples.
and System Interconnections -- 11.3 Fundamental Theorem of Linear Equations (Review) -- 11.4 Reachability and Controllability Gramians -- 11.5 Open-Loop Minimum-Energy Control -- 11.6 Controllability Matrix (LTI) -- 11.7 Discrete-Time Case -- 11.8 MATLAB® Commands -- 11.9 Practice Exercise -- 11.10 Exercises -- 12 CONTROLLABLE SYSTEMS -- 12.1 Controllable Systems -- 12.2 Eigenvector Test for Controllability -- 12.3 Lyapunov Test for Controllability -- 12.4 Feedback Stabilization Based on the Lyapunov Test -- 12.5 Eigenvalue Assignment -- 12.6 Practice Exercises -- 12.7 Exercises -- 13 CONTROLLABLE DECOMPOSITIONS -- 13.1 Invariance with Respect to Similarity Transformations -- 13.2 Controllable Decomposition -- 13.3 Block Diagram Interpretation -- 13.4 Transfer Function -- 13.5 MATLAB® Commands -- 13.6 Exercise -- 14 STABILIZABILITY -- 14.1 Stabilizable System -- 14.2 Eigenvector Test for Stabilizability -- 14.3 Popov-Belevitch-Hautus (PBH) Test for Stabilizability -- 14.4 Lyapunov Test for Stabilizability -- 14.5 Feedback Stabilization Based on the Lyapunov Test -- 14.6 MATLAB® Commands -- 14.7 Exercises -- IV OBSERVABILITY AND OUTPUT FEEDBACK -- 15 OBSERVABILITY -- 15.1 Motivation: Output Feedback -- 15.2 Unobservable Subspace -- 15.3 Unconstructible Subspace -- 15.4 Physical Examples -- 15.5 Observability and Constructibility Gramians -- 15.6 Gramian-Based Reconstruction -- 15.7 Discrete-Time Case -- 15.8 Duality for LTI Systems -- 15.9 Observability Tests -- 15.10 MATLAB® Commands -- 15.11 Practice Exercises -- 15.12 Exercises -- 16 OUTPUT FEEDBACK -- 16.1 Observable Decomposition -- 16.2 Kalman Decomposition Theorem -- 16.3 Detectability -- 16.4 Detectability Tests -- 16.5 State Estimation -- 16.6 Eigenvalue Assignment by Output Injection -- 16.7 Stabilization through Output Feedback -- 16.8 MATLAB® Commands -- 16.9 Exercises -- 17 MINIMAL REALIZATIONS -- 17.1 Minimal Realizations -- 17.2 Markov Parameters -- 17.3 Similarity of Minimal Realizations -- 17.4 Order of a Minimal SISO Realization -- 17.5 MATLAB® Commands -- 17.6 Practice Exercises -- 17.7 Exercises -- LINEAR SYSTEMS II — ADVANCED MATERIAL -- V POLES AND ZEROS OF MIMO SYSTEMS -- 18 SMITH-MCMILLAN FORM -- 18.1 Informal Definition of Poles and Zeros -- 18.2 Polynomial Matrices: Smith Form -- 18.3 Rational Matrices: Smith-McMillan Form -- 18.4 McMillan Degree, Poles, and Zeros -- 18.5 Blocking Property of Transmission Zeros -- 18.6 MATLAB® Commands -- 18.7 Exercises -- 19 STATE-SPACE POLES, ZEROS, AND MINIMALITY -- 19.1 Poles of Transfer Functions versus Eigenvalues of State-Space Realizations -- 19.2 Transmission Zeros of Transfer Functions versus Invariant Zeros of State-Space Realizations -- 19.3 Order of Minimal Realizations -- 19.4 Practice Exercises -- 19.5 Exercise -- 20 SYSTEM INVERSES -- 20.1 System Inverse -- 20.2 Existence of an Inverse -- 20.3 Poles and Zeros of an Inverse -- 20.4 Feedback Control of Invertible Stable Systems with Stable Inverses -- 20.5 MATLAB® Commands .
-- 20.6 Exercises -- VI LQR/LQG OPTIMAL CONTROL -- 21 LINEAR QUADRATIC REGULATION (LQR) -- 21.1 Deterministic Linear Quadratic Regulation (LQR) -- 21.2 Optimal Regulation -- 21.3 Feedback Invariants -- 21.4 Feedback Invariants in Optimal Control -- 21.5 Optimal State Feedback -- 21.6 LQR in MATLAB® -- 21.7 Additional Notes -- 21.8 Exercises -- 22 THE ALGEBRAIC RICCATI EQUATION (ARE) -- 22.1 The Hamiltonian Matrix -- 22.2 Domain of the Riccati Operator -- 22.3 Stable Subspaces -- 22.4 Stable Subspace of the Hamiltonian Matrix -- 22.5 Exercises -- 23 FREQUENCY DOMAIN AND ASYMPTOTIC PROPERTIES OF LQR -- 23.1 Kalman’s Equality -- 23.2 Frequency Domain Properties: Single-Input Case -- 23.3 Loop Shaping Using LQR: Single-Input Case -- 23.4 LQR Design Example -- 23.5 Cheap Control Case -- 23.6 MATLAB® Commands -- 23.7 Additional Notes -- 23.8 The Loop-Shaping Design Method (Review) -- 23.9 Exercises -- 24 OUTPUT FEEDBACK -- 24.1 Certainty Equivalence -- 24.2 Deterministic Minimum-Energy Estimation (MEE) -- 24.3 Stochastic Linear Quadratic Gaussian (LQG) Estimation -- 24.4 LQR/LQG Output Feedback -- 24.5 Loop Transfer Recovery (LTR) -- 24.6 Optimal Set-Point Control -- 24.7 LQR/LQG with MATLAB® -- 24.8 LTR Design Example -- 24.9 Exercises -- 25 LQG/LQR AND THE Q PARAMETERIZATION -- 25.1 Q-Augmented LQG/LQR Controller -- 25.2 Properties -- 25.3 Q Parameterization -- 25.4 Exercise -- 26 Q DESIGN -- 26.1 Control Specifications for Q Design -- 26.2 The Q Design Feasibility Problem -- 26.3 Finite-Dimensional Optimization: Ritz Approximation -- 26.4 Q Design Using MATLAB® and CVX -- 26.5 Q Design Example -- 26.6 Exercise -- BIBLIOGRAPHY -- INDEX -- .
