Preface THREE TERM CONTROLLERS PID Controllers: An Overview of Classical Theory Introduction to Control The Magic of Integral Control PID Controllers Classical PID Controller Design Integrator Windup PID Controllers for Delay-Free LTI Systems Introduction Stabilizing Set Signature Formulas Computation of the PID Stabilizing Set PID Design with Performance Requirements PID Controllers for Systems with Time Delay Introduction Characteristic Equations for Delay Systems The Padé Approximation and Its Limitations The Hermite-Biehler Theorem for Quasipolynomials Stability of Systems with a Single Delay PID Stabilization of First-Order Systems with Time Delay PID Stabilization of Arbitrary LTI Systems with a Single Time Delay Proofs of Lemmas 3.3, 3.4, and 3.5 Proofs of Lemmas 3.7 and 3.9 An Example of Computing the Stabilizing Set Digital PID Controller Design Introduction Preliminaries Tchebyshev Representation and Root Clustering Root Counting Formulas Digital PI, PD, and PID Controllers Computation of the Stabilizing Set Stabilization with PID Controllers First-Order Controllers for LTI Systems Root Invariant Regions An Example Robust Stabilization by First-Order Controllers Hinfinity Design with First-Order Controllers First-Order Discrete-Time Controllers Controller Synthesis Free of Analytical Models Introduction Mathematical Preliminaries Phase, Signature, Poles, Zeros, and Bode Plots PID Synthesis for Delay-Free Continuous-Time Systems PID Synthesis for Systems with Delay PID Synthesis for Performance An Illustrative Example: PID Synthesis Model-Free Synthesis for First-Order Controllers Model-Free Synthesis of First-Order Controllers for Performance Data-Based Design vs. Model-Based Design Data-Robust Design via Interval Linear Programming Computer-Aided Design Data-Driven Synthesis of Three Term Digital Controllers Introduction Notation and Preliminaries PID Controllers for Discrete-Time Systems Data-Based Design: Impulse Response Data First-Order Controllers for Discrete-Time Systems Computer-Aided Design ROBUST PARAMETRIC CONTROL Stability Theory for Polynomials Introduction The Boundary Crossing Theorem The Hermite-Biehler Theorem Schur Stability Test Hurwitz Stability Test Stability of a Line Segment Introduction Bounded Phase Conditions Segment Lemma Schur Segment Lemma via Tchebyshev Representation Some Fundamental Phase Relations Convex Directions The Vertex Lemma Stability Margin Computation Introduction The Parametric Stability Margin Stability Margin Computation The Mapping Theorem Stability Margins of Multilinear Interval Systems Robust Stability of Interval Matrices Robustness Using a Lyapunov Approach Stability of a Polytope Introduction Stability of Polytopic Families The Edge Theorem Stability of Interval Polynomials Stability of Interval Systems Polynomic Interval Families Robust Control Design Introduction Interval Control Systems Frequency Domain Properties Nyquist, Bode, and Nichols Envelopes Extremal Stability Margins Robust Parametric Classical Design Robustness under Mixed Perturbations Robust Small Gain Theorem Robust Performance The Absolute Stability Problem Characterization of the SPR Property The Robust Absolute Stability Problem OPTIMAL AND ROBUST CONTROL The Linear Quadratic Regulator An Optimal Control Problem The Finite Time LQR Problem The Infinite Horizon LQR Problem Solution of the Algebraic Riccati Equation The LQR as an Output Zeroing Problem Return Difference Relations Guaranteed Stability Margins for the LQR Eigenvalues of the Optimal Closed Loop System Optimal Dynamic Compensators Servomechanisms and Regulators SISO HinfinityAND l1OPTIMAL CONTROL Introduction The Small Gain Theorem LStability and Robustness via the Small Gain Theorem YJBK Parametrization of All Stabilizing Compensators (Scalar Case) Control Problems in the HinfinityFramework HinfinityOptimal Control: SISO Case l1Optimal Control: SISO Case HinfinityOptimal Multivariable Control HinfinityOptimal Control Using Hankel Theory The State Space Solution of Hinfinity Optimal Control Appendix A: Signal Spaces Vector Spaces and Norms Metric Spaces Equivalent Norms and Convergence Relations between Normed Spaces Appendix B: Norms for Linear Systems Induced Norms for Linear Maps Properties of Fourier and Laplace Transforms Lp/lpNorms of Convolutions of Signals Induced Norms of Convolution Maps EPILOGUE Robustness and Fragility Feedback, Robustness, and Fragility Examples Discussion References Index Exercises, Notes, and References appear at the end of each chapter. ations The Hermite-Biehler Theorem for Quasipolynomials Stability of Systems with a Single Delay PID Stabilization of First-Order Systems with Time Delay PID Stabilization of Arbitrary LTI Systems with a Single Time Delay Proofs of Lemmas 3.

3, 3.4, and 3.5 Proofs of Lemmas 3.7 and 3.9 An Example of Computing the Stabilizing Set Digital PID Controller Design Introduction Preliminaries Tchebyshev Representation and Root Clustering Root Counting Formulas Digital PI, PD, and PID Controllers Computation of the Stabilizing Set Stabilization with PID Controllers First-Order Controllers for LTI Systems Root Invariant Regions An Example Robust Stabilization by First-Order Controllers Hinfinity Design with First-Order Controllers First-Order Discrete-Time Controllers Controller Synthesis Free of Analytical Models Introduction Mathematical Preliminaries Phase, Signature, Poles, Zeros, and Bode Plots PID Synthesis for Delay-Free Continuous-Time Systems PID Synthesis for Systems with Delay PID Synthesis for Performance An Illustrative Example: PID Synthesis Model-Free Synthesis for First-Order Controllers Model-Free Synthesis of First-Order Controllers for Performance Data-Based Design vs. Model-Based Design Data-Robust Design via Interval Linear Programming Computer-Aided Design Data-Driven Synthesis of Three Term Digital Controllers Introduction Notation and Preliminaries PID Controllers for Discrete-Time Systems Data-Based Design: Impulse Response Data First-Order Controllers for Discrete-Time Systems Computer-Aided Design ROBUST PARAMETRIC CONTROL Stability Theory for Polynomials Introduction The Boundary Crossing Theorem The Hermite-Biehler Theorem Schur Stability Test Hurwitz Stability Test Stability of a Line Segment Introduction Bounded Phase Conditions Segment Lemma Schur Segment Lemma via Tchebyshev Representation Some Fundamental Phase Relations Convex Directions The Vertex Lemma Stability Margin Computation Introduction The Parametric Stability Margin Stability Margin Computation The Mapping Theorem Stability Margins of Multilinear Interval Systems Robust Stability of Interval Matrices Robustness Using a Lyapunov Approach Stability of a Polytope Introduction Stability of Polytopic Families The Edge Theorem Stability of Interval Polynomials Stability of Interval Systems Polynomic Interval Families Robust Control Design Introduction Interval Control Systems Frequency Domain Properties Nyquist, Bode, and Nichols Envelopes Extremal Stability Margins Robust Parametric Classical Design Robustness under Mixed Perturbations Robust Small Gain Theorem Robust Performance The Absolute Stability Problem Characterization of the SPR Property The Robust Absolute Stability Problem OPTIMAL AND ROBUST CONTROL The Linear Quadratic Regulator An Optimal Control Problem The Finite Time LQR Problem The Infinite Horizon LQR Problem Solution of the Algebraic Riccati Equation The LQR as an Output Zeroing Problem Return Difference Relations Guaranteed Stability Margins for the LQR Eigenvalues of the Optimal Closed Loop System Optimal Dynamic Compensators Servomechanisms and Regulators SISO HinfinityAND l1OPTIMAL CONTROL Introduction The Small Gain Theorem LStability and Robustness via the Small Gain Theorem YJBK Parametrization of All Stabilizing Compensators (Scalar Case) Control Problems in the HinfinityFramework HinfinityOptimal Control: SISO Case l1Optimal Control: SISO Case HinfinityOptimal Multivariable Control HinfinityOptimal Control Using Hankel Theory The State Space Solution of Hinfinity Optimal Control Appendix A: Signal Spaces Vector Spaces and Norms Metric Spaces Equivalent Norms and Convergence Relations between Normed.