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

This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

Linear Robust Control

This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

A lifting technique for linear periodic systems with applications to sampled-data control

Parametrization of F1 and Sf Controllers In H∞ Control Problems

In this paper, a simple derivation of the Riccati equation based solutions to the standard H ∞ control problem, namely the well-known Glover-Doyle solution and DGKF solution is given based on LMI solution. It is hoped that this will be helpful for ordinary control engineers in deepening the understanding of Riccati equation solutions.

http://ieeexplore.ieee.org/iel7/7084796/7084797/07085110.pdf

A simple derivation of are solutions to the standard H ∞ control problem based on LMI solution

In this paper, a discontinuous nonlinear control approach is proposed for the stabilization control of a class of nonholonomic systems which include the steering of two-wheel and four-wheel cars. This approach is capable of realizing either global finite time stability or uniformly globally ultimate boundedness. Further, in the applications to the steering control of vehicles, it is shown how to incorporate physical intuition into design so as to obtain continuous inputs that can be implemented.

http://ieeexplore.ieee.org/iel5/7520/20470/00945942.pdf

Steering control of vehicles by discontinuous control approach

This paper proposes two high performance control methods and an on-line load identification algorithm for boost DC-DC converters. The first is a short-horizon model predictive control method whose solution can be computed analytically, thus rendering an algorithm that can be implemented on-line. Further, we show how to find a suitable performance index so as to achieve good response. The idea is to use the inductance current as the penalized output, instead of the output voltage. The second is a 3-level hysteresis control method which is a natural extension of the conventional hysteresis control method and has three layers in the hysteresis band. The key is to set the duty ratio in the central layer as the steady-state duty ratio. Compared with the well-known PID-PWM method, the proposed methods are able to achieve a better trade-off between rise-time and overshoot in the response of output voltage. Finally, a simple on-line identification algorithm is proposed for the load resistance. Combination of the proposed control methods and identification algorithm yields high performance robust control for boost converters.

High performance algorithms for the control and load identification of boost DC-DC converters

In the robust control of systems with dynamic uncertainty, there are mainly two methodologies: one based on the gain bound of uncertainty and the other based on the phase bound. The well-known small-gain approach belongs to the former and is able to conduct nonconservative robust performance design by using $\mu$ -synthesis. Meanwhile, the study on the latter case is still under way, and only a positive-real method was proposed by the authors recently to handle the robust performance synthesis. This paper aims at improving the positive-real method. The key idea is to model a passive uncertainty not only by its phase bound but also utilizing its largest gain. This is achieved by applying the notion of output strict passivity well known in nonlinear control. Furthermore, the negative-imaginary uncertainty can be treated in this framework more naturally. A case study on a vibration system validates the advantage of the present method.

Kang-Zhi Liu

Papers

Parametrization of F1 and Sf Controllers In H∞ Control Problems

A simple derivation of are solutions to the standard H ∞ control problem based on LMI solution

Steering control of vehicles by discontinuous control approach

High performance algorithms for the control and load identification of boost DC-DC converters

Robust Performance Design for Systems With Output Strictly Passive Uncertainty