1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.

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Essentials of Robust Control

https://www.control.utoronto.ca/people/profs/francis/dft.pdf

Feedback Control Theory

This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of robustness problems, periodic compensators are superior to time-invariant ones. We will give explicit design techniques which can be easily implemented. In the context of periodic controllers, we also consider the strong and simultaneous stabilization problems. Finally, we show that for the problem of weighted sensitivity minimization for linear time-invariant plants, time-varying controllers offer no advantage over the time-invariant ones.

Robust control of linear time-invariant plants using periodic compensation

An integrated approach to the design of practical adaptive control algorithms is presented. Many existing ideas are brought together, and the effect of various design parameters available to a user is explored. The theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators. It is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics. >

Design issues in adaptive control

In this paper, we look for feedbacks that minimize the sensitivity function of a linear single-variable feedback system represented by its frequency responses. Sensitivity to disturbances and robustness under plant perturbations are measured in a weighted H^{\infty} norm. In an earlier paper, Zames proposed an approach to feedback design involving the measurement of sensitivity by "multiplicative seminorms," which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty, or where signal power-spectra are not fixed, but belong to sets. The problem was studied in a general setting, and some H^{\infty} examples were solved. Here, a detailed study of the single-variable case is undertaken. The results are extended to unstable plants, and explicit formulas for the general situation of a finite number of right half-plane (RHP) plant zeros or poles are provided. The Q or "approximate-inverse" parametrization of feedbacks that maintain closed-loop stability is extended to the ease of unstable plants. The H^{\infty} and Wiener-Hopf approaches are compared.

Feedback, minimax sensitivity, and optimal robustness

The problem of designing a feedback system with prescribed properties is attacked via a fractional representation approach to feedback system analysis and synthesis. To this end we let H denote a ring of operators with the prescribed properties and model a given plant as the ratio of two operators in H . This, in turn, leads to a simplified test to determine whether or not a feedback system in which that plant is embedded has the prescribed properties and a complete characterization of those compensators which will "place" the feedback system in H . The theory is formulated axiomatically to permit its application in a wide variety of system design problems and is extremely elementary in nature requiring no more than addition, multiplication, subtraction, and inversion for its derivation even in the most general settings.

Feedback system design: The fractional representation approach to analysis and synthesis

An explicit relationship between the fractional representation approach feedback system design and the algebro-geometric approach to system theory, is formulated and used to derive a global solution to the feedback system problem. These techniques are then applied to the simultaneous stabilization problem, yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator.

Fractional representation, algebraic geometry, and the simultaneous stabilization problem

The problem of designing a feedback controller which stabilizes a number of plants simultaneously is discussed from the fractional representation point of view. An abstract solution of this general simultaneous stabilization problem is presented, and an elementary, explicit criterion is given for the simulteneous stabilizability of two systems. Finally, some examples and counter examples are presented, and some open problems are discussed.

J. Murray

Papers

Feedback system design: The fractional representation approach to analysis and synthesis

Fractional representation, algebraic geometry, and the simultaneous stabilization problem

Simultaneous design of control systems