Robust Control

Foreword. Preface. 0. Background and Motivation. Introduction to Control. Historical Background. The Parametric Theory. Discussion of Contents. Notes and References. 1. Stability Theory via the Boundary Crossing Theorem. Introduction. The Boundary Crossing Theorem. The Hermite- Biehler Theorem. Schur Stability Test. Hurwitz Stability Test. A Few Complements. Exercises. Notes and References. 2. Stability of a Line Segment. Introduction. Bounded Phase Conditions. Segment Lemma. Some Fundamental Phase Relations. Convex Directions. The Vertex Lemma. Exercises. Notes and References. 3. The Stability Ball in Coefficient Space. Introduction. The Ball of Stable Polynomials. The Real l-2 Stability Ball. The Tsypkin-Polyak Locus: l-p Stability Ball. Robust Stability of Disc Polynomials. Exercises. Notes and References. 4. The Parametric Stability Margin. Introduction. The Stability Ball in Parameter Space. The Image Set Approach. Stability Margin Computation in the Linear Case. l-2 Stability Margin. l-infinity and l-1 Stability Margins. Polytopic Families. Extremal Properties of Edges and Vertices. The Tsypkin- Polyak Plot. Robust Stability of Linear Disc Polynomials. Exercises. Notes and References. 5. Interval Polynomials: Kharitonovs Theorem. Introduction. Kharitonovs Theorem for Real Polynomials. Kharitonovs Theorem for Complex Polynomials. Interlacing and Image Set Interpretation. Extremal Properties of the Kharitonov Polynomials. Robust State-Feedback Stabilization. Polynomial Functions of Interval Polynomials. Schur Stability of Interval Polynomials. Exercises. Notes and References. 6. The Edge Theorem. Introduction. The Edge Theorem. Examples. Extensions of Edge Results. Exercises. Notes and References. 7. The Generalized Kharitonov Theorem. Introduction. Problem Formulation and Notation. The Generalized Kharitonov Theorem. Examples. Image Set Interpretation. Extension to Complex Quasipolynomials. sigma and theta Hurwitz Stability of Interval Polynomials. Exercises. Notes and References. 8. Frequency Domain Properties of Linear Interval Systems. Introduction. Interval Control Systems. Frequency Domain Properties. Nyquist, Bode, and Nichols Envelopes. Extremal Stability Margins. Linear Interval Control Systems. Polytopic Systems. Linear Fractional Transformation. Robust Parametric Classical Design. Exercises. Notes and References. 9. Robust Stability and Performance Under Mixed Pertubations. Introduction. Small Gain Theorem. Small Gain Theorem for Interval Systems. Robust Small Gain Theorem. Robust Performance. Vertex Results for Extremal H-infinity Norms. The Absolute Stability Problem. Characterization of the SPR Property. The Robust Absolute Stability Problem. Exercises. Notes and References. 10. Multilinear Interval Systems: The Mapping Theorem. Introduction. The Mapping Theorem. Robust Stability Via the Mapping Theorem. Multilinear Interval Systems. Examples. Exercises. Notes and References. 11. Frequency Domain Properties of Multilinear Interval Systems. Introduction. Multilinear Interval Polynomials. Parametric Stability Margin. Multilinear Interval Systems. H-infinity Stability Margin. Nonlinear Sector Bounded Stability Margin. Interval Plants and Diagonal Representation. Exercises. Notes and References. 12. State Space Parameter Perturbations. Introduction. State Space Perturbations. Robust Stability of Interval Matrices. Robustness Using a Lyapunov Approach. The Matrix Stability Radius Problem. Two Special Classes of Interval Matrices. Exercises. Notes and References. 13. Robust Parametric Stabilization. Introduction. Simultaneous Strong Stabilization. Internal Stability and the Q Parameterization. Robust Stabilization: Unstructured Pertubations. Nevanlinna-Pick Interpolation. Overbounding Parametric Uncertainty. Robust Stabilization: State Space Solution. A Robust Stability Bound for Interval Systems. Exercises. Notes and References. 14. Interval Modelling, Identification and Control. Introduction. Interval Modelling with a Single Data Set. Application to a Mini-Mast System. Vibration Suppression Control of a Structure. Notes and References. References. Author Index. Subject Index.