Robust Stabilisation and H_ Problems - Adrian-Mihail Stoica

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Résumé :
This book contains the combined treatment of several problems of control systems theory, such as the emH/emINFINITY control problem, the Nehari problem and robust stabilisation. These topics are described from a new perspective which is essentially created by an original generalisation of the algebraic Riccati theory to the indefinite sign case. br/ The theory is developed using methods including the Popov function, the Kalman-Popov-Yakubovich system in emJ/em-form, and the extended Hamiltonian pencil. The signature condition on the Popov function plays a crucial role in providing the unified approach to solving the control problems considered. Particular attention is paid to the optimal solutions of the emH/emINFINITY control problem and the Nehari problem for which a singular perturbation-based technique is employed to derive explicit well-conditioned computational formulae. Numerical examples, mainly from aeronautics, illustrate the performances of the proposed procedures and design algorithms. br/ emAudience:/em This volume will be of interest to researchers, graduate students and control engineers working in systems and control theory, mathematical systems theory, optimal control, aerospace engineering and numerical analysis.

Sommaire:
1 Linear Systems: Some Prerequisites.- 1.1 State Space Description and Input/Output Map.- 1.2 Dichotomy. RL?, RH+? and RH?? Spaces.- 1.3 Hankel and Toeplitz Operators.- 1.4 Balanced Forms.- Notes and References.- 2 The Kalman-Popov-Yakubovich System of Indefinite Sign.- 2.1 Popov Triplets: Associated Objects, Equivalence, Duality.- 2.2 Basic Operators.- 2.3 The Stabilizing Solution.- 2.4 A Matrix Pencil Description.- 2.5 The Signature Condition.- Notes and References.- 3 H? Control: A Signature Condition Based Approach.- 3.1 Problem Statement.- 3.2 The Redheffer Theorem.- 3.3 A First Set of Necessary Solvability Conditions.- 3.4 A Second Set of Necessary Solvability Conditions.- 3.5 Coupled and Uncoupled Necessity Solvability Conditions.- 3.6 Sufficient Solvability Conditions: An Explicit Solution in KPYS Terms.- 3.7 Singular Problems: Necessary and Sufficient Conditions.- Notes and References.- 4 The Nehari Problem.- 4.1 The Two-Block Case.- 4.2 The One-Block Case.- Notes and References.- 5 Optimal H? Problems: A Singular Perturbation Approach.- 5.1 Optimal Solution of the H?- Control Problem.- 5.2 Case Studies.- Notes and References.- 6 Singular H? Problems.- 6.1 Robustness with Respect to Multiplicative Uncertainty.- 6.2 Sensitivity Minimization.- Notes and References.