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

Head Positioning Control of a Hard Disk Drive Using H ∞ Control Theory

In this paper, a method for automatic parking systems is proposed based on the approach of Liu (2002) and the corresponding system package is developed. This method is composed of control laws for the steering angle and the driving velocity, algorithms for various kinds of parking tasks under steering angle and parking space limitations. The system works pretty well in experiments subject to various parking situations.

Development of an auto-parking system with physical limitations

In many real-world rotary machines, there is an inherent need to attenuate time-varying but position-dependent periodic disturbances. This article proposes an improved repetitive controller, in which a spatial internal model, a spatial low-pass filter, and a frequency alignment are synthesized. The controller is digitally implemented in a uniform time-sampling system. Specifically, a universal internal model of arbitrary periodic signal in spatial domain is derived for the attenuation of the position-dependent disturbances in the rotary machine, and a spatial low-pass filter is designed for the stability of the closed-loop system. Furthermore, a frequency alignment strategy is designed to compensate the bias resulted from the filter. Moreover, the cascaded utilization of the proposed controllers is introduced to improve the performance of a position-feedback servo system. Experimental verification and comparisons validate the feasibility and effectiveness of the proposed method in both single and cascaded configurations.

Attenuation of Position-Dependent Periodic Disturbance for Rotary Machines by Improved Spatial Repetitive Control With Frequency Alignment

We establish conjugation notion in discrete-time systems, first introduced into the H ∞ control theory of continuous-time systems by Kimura (1989). In discrete-time systems, conjugation is a very elementary operation on rational transfer functions that replaces some of their poles by their reflections with respect to the unit circle. With the aid of J-lossless conjugation conjugation by a J.lossless system), it is shown that the parametrization of sub-optimal solutions of H ∞ model-matching problems is reduced to a Lyapunov-type equation. The parametrization of all solutions is given in an extremely simple way. It is further proved that the J-lossless conjugation of the H ∞ model-matching problem is a natural state-space representation of classical interpolation in discrete-time systems.

Kang-Zhi Liu

Papers

Head Positioning Control of a Hard Disk Drive Using H ∞ Control Theory

Development of an auto-parking system with physical limitations

Attenuation of Position-Dependent Periodic Disturbance for Rotary Machines by Improved Spatial Repetitive Control With Frequency Alignment

Conjugation and H ∞ control of discrete-time systems

H∞ control with weighting functions having purely imaginary poles—implementing internal models to H∞ controllers