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

In this paper, a nonlinear output feedback control method is proposed for a magnetic bearing system which has a strong nonlinearity in the magnetic bearing system which has a strong nonlinearity in the magnetic actuator. The basic idea is to make full use of the feature that the dynamics part is linear and hence can be stabilized by output of the actuator is regarded as a virtual input. Then it is shown that the backstepping and completing square techniques enable the construction of the construction of the real input using measured output only.

/pdf/a-nonlinear-output-feedback-control-method-for-magnetic-119xjv5oil.pdf

A nonlinear output feedback control method for magnetic bearing systems

Summary

The well-known small-gain and passivity approaches to robust control only make use of either the gain or the phase information of uncertainty in system design. This results in a limitation on the achievable control bandwidth in practical applications. To relax the limitations associated with these approaches, we explore the possibility of utilizing both the gain and the phase information of uncertainty in robust control design. In this paper, the modeling of uncertainty accounting for both gain and phase is discussed first. Then conditions for robust stability and robust performance (sensitivity and bandwidth) are derived respectively. These robustness conditions are described as phase or gain constraints on the nominal system in different frequency bands. Further, it is revealed, both theoretically and via a hard disk drive benchmark, that a much higher robust performance can be achieved by using the gain and phase information of uncertainty. Copyright © 2013 John Wiley & Sons, Ltd.

A high-performance robust control method based on the gain and phase information of uncertainty

This paper is concerned with the analysis of the stability common to linear regulator and servomechanism problems, called comprehensive stability, in a unified framework. The necessary and sufficient condition is derived and the parameterization of a class of controllers satisfying such stability given. This work is believed to lay a foundation for a unified theory of regulator and servomechanism. >

A unified stability analysis for linear regulator and servomechanism problems

Neo-robust control is a new theory proposed by the authors, which utilizes both the gain and the phase information of uncertainty in robust control design. In this paper, we extend the idea of neo-robust control to a class of uncertain systems with factorized uncertainty. This class of systems is good at describing the uncertainties arising in process control systems. Conditions on robust stability, the robust sensitivity and the robust bandwidth are derived. All these results are described in terms of the gain and phase conditions on the nominal loop gain which is very convenient for loop shaping design. Further, a numerical example is shown to illustrate the design process.

Kang-Zhi Liu

Papers

A nonlinear output feedback control method for magnetic bearing systems

A high-performance robust control method based on the gain and phase information of uncertainty

A unified stability analysis for linear regulator and servomechanism problems

Neo-robust control theory for factorized uncertainty

A new spatial modeling method for 3D formation drillability field using fuzzy c-means clustering and random forest