There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

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Stability of Time-Delay Systems

There is an increasing demand for dynamic systems to become safer and more reliable This requirement extends beyond the normally accepted safety-critical systems such as nuclear reactors and aircraft, where safety is of paramount importance, to systems such as autonomous vehicles and process control systems where the system availability is vital It is clear that fault diagnosis is becoming an important subject in modern control theory and practice Robust Model-Based Fault Diagnosis for Dynamic Systems presents the subject of model-based fault diagnosis in a unified framework It contains many important topics and methods; however, total coverage and completeness is not the primary concern The book focuses on fundamental issues such as basic definitions, residual generation methods and the importance of robustness in model-based fault diagnosis approaches In this book, fault diagnosis concepts and methods are illustrated by either simple academic examples or practical applications The first two chapters are of tutorial value and provide a starting point for newcomers to this field The rest of the book presents the state of the art in model-based fault diagnosis by discussing many important robust approaches and their applications This will certainly appeal to experts in this field Robust Model-Based Fault Diagnosis for Dynamic Systems targets both newcomers who want to get into this subject, and experts who are concerned with fundamental issues and are also looking for inspiration for future research The book is useful for both researchers in academia and professional engineers in industry because both theory and applications are discussed Although this is a research monograph, it will be an important text for postgraduate research students world-wide The largest market, however, will be academics, libraries and practicing engineers and scientists throughout the world

Robust Model-Based Fault Diagnosis for Dynamic Systems

Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies

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A Survey of Recent Results in Networked Control Systems

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 note focuses on deriving stability conditions for a class of linear parameter-dependent systems in a state-space representation. More precisely, we will compute the set of parameters for which the characteristic roots are located on the imaginary axis, and next we will give the characterization of the way such critical roots are crossing the imaginary axis. The methodology considered makes use of the computation of the generalized eigenvalues of an appropriate matrix pencil combined with an operator perturbation approach for deriving the crossing direction. Finally, the particular case of parameter-dependent polynomials will be also considered, and the stability analysis of time-delay systems is also revisited in this perspective.

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On the robust stability of some parameter-dependent linear systems: solutions via matrix pencil techniques

A Modified Separated-Bias Estimation Approach to the Detection and Estimation of Failures in Linear Systems

In this paper, we discover that the trace of the division of the optimal output estimation error covariance over the noise covariance attained by the Kalman-Bucy filter can be explicitly expressed in terms of the plant dynamics and noise statistics in a frequency-domain integral characterization. Towards this end, we examine the algebraic Riccati equation associated with Kalman-Bucy filtering using analytic function theory and relate it to the Bode integral. Our approach features an alternative, frequency-domain framework for analyzing algebraic Riccati equations and reduces to various existing related results.

A Frequency-Domain Characterization of Optimal Error Covariance for the Kalman-Bucy Filter

Azimuth multi-channel technology has been widely used in high-resolution wide-swath synthetic aperture radar (SAR). However, for airborne multi-channel SAR, motion error decreases image quality seriously, including resolution loss and false target appearance. In this paper, a multi-channel SAR imaging method is proposed combined with improved two-step motion compensation. First, multi-channel SAR motion error geometric model is established and the range-invariant channel-dependent phase error is derived. After that the range-dependent phase error for different channels is analyzed in detail. Then, the multi-channel imaging method with motion compensation is addressed. Finally, airborne SAR data is used to validate the proposed method. Processing results show that the proposed method can correct motion error and improve image quality effectively.

An Airborne Multi-Channel Sar Imaging Method with Motion Compensation

This paper attempts to give a thorough treatment of the performance limitation of a linear time invariant multivariable system in tracking a reference signal which is a linear combination of a step signal and several sinusoids with different frequencies. The tracking performance is measured by an integral square error between the output of the plant and the reference signal. Our purpose is to find the fundamental limitation for the attainable tracking performance, under any control structure and parameters, in terms of the characteristics and structural parameters of the given plant, as well as those of the reference signal under consideration. It is shown that this fundamental limitation depends on the interaction between the reference signal and the nonminimum phase zeros of the plant and their frequency-dependent directional information. The main results of this paper are based on the assumption that the controller accesses the full information of the reference. However, when the full information of the reference is unavailable, we also obtain a simple performance limit, for an important special case, which clearly shows the extra cost one has to pay due to the information restriction.

Jie Chen

Papers

On the robust stability of some parameter-dependent linear systems: solutions via matrix pencil techniques

A Modified Separated-Bias Estimation Approach to the Detection and Estimation of Failures in Linear Systems

A Frequency-Domain Characterization of Optimal Error Covariance for the Kalman-Bucy Filter

An Airborne Multi-Channel Sar Imaging Method with Motion Compensation

Fundamental performance limitations in tracking and sinusoidal signals