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

Long time coherent integration is a vital method for improving the detection ability of global navigation satellite system (GNSS)-based passive radar, because the GNSS signal is not radar-designed and its power level is very low For aircraft detection, the large range cell migration (RCM) and Doppler frequency migration (DFM) will seriously affect the coherent processing of azimuth signals, and the traditional range match filter will also be mismatched due to the Doppler-intolerant characteristic of GNSS signals Accordingly, the energy loss of 2-dimensional (2-D) coherent processing is inevitable in traditional methods In this paper, a novel 2-D coherent integration processing and algorithm for aircraft target detection is proposed For azimuth processing, a modified Radon Fourier Transform (RFT) with range-walk removal and Doppler rate estimation is performed In respect to range compression, a modified matched filter with a shifting Doppler is applied As a result, the signal will be accurately focused in the range-Doppler domain, and a sufficiently high SNR can be obtained for aircraft detection with a moving target detector Numerical simulations demonstrate that the range-Doppler parameters of an aircraft target can be obtained, and the position and velocity of the aircraft can be estimated accurately by multiple observation geometries due to abundant GNSS resources The experimental results also illustrate that the blind Doppler sidelobe is suppressed effectively and the proposed algorithm has a good performance even in the presence of Doppler ambiguity

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2-D Coherent Integration Processing and Detecting of Aircrafts Using GNSS-Based Passive Radar

In this paper we study stability properties of linear time-delay systems with commensurate delays. We investigate specifically the asymptotic behavior of the critical characteristic zeros of time-delay systems on the imaginary axis. This behavior determines whether the imaginary zeros cross from one half plane into another, and hence plays a critical role in determining the stability of a time-delay system. We emphasize in particular the second-order asymptotic properties, which, together with earlier results on first-order analysis, provide a more complete characterization of the zero asymptotic behavior.

High-Order Analysis Of Critical Stability Properties of Linear Time-Delay Systems

This paper studies fixed-time stabilization (FxTS) of a general controllable linear system with an input delay τ. It is shown that such a problem is not solvable if the prescribed convergence time $T_{τ}$ is smaller than $2_{τ}$ 
. For $T_{τ} ≥ 3_{τ}$ 
, a solution based on linear periodic delayed feedback (PDF) without any distributed delay is established. For $T_{τ} > 2_{τ}$ 
, a solution based on linear predictor-based PDF containing a distributed delay is proposed. For both cases, the gains of the PDF can be chosen as continuous, continuously differentiable, and even smooth, in the sense of infinitely many times differentiable. If only an output signal is available for feedback, two classes of linear observers with periodic coefficients are designed so that their states converge to the current and future states of the system at a prescribed finite time, respectively. With the observed current and future states, FTS can also be achieved by using respectively the PDF and observer-based PDF. A linear periodic feedback (without delay) is also established to solve the FxTS problem of linear systems with both instantaneous and delayed controls, which cannot be stabilized by any constant instantaneous feedback in certain cases. Two numerical examples verify the effectiveness of the proposed approaches.

Fixed-time stabilization of linear delay systems by smooth periodic delayed feedback

For part 1, see Proc. of 35th IEEE Conference on Decision and Control, p.726-31 (1996). This paper continues the earlier work on optimal tracking problems with respect to multivariable feedback systems. We examine the error between a system's output response and its command input, which is either a sinusoidal or a ramp signal. This error is quantified under an integral square criterion, and is adopted as a measure of tracking accuracy. For both sinusoidal and ramp signals, we derive explicit expressions of the minimal tracking error attainable by all possible stabilizing controllers. These results show that the tracking accuracy may be fundamentally limited by plant nonminimum phase zeros and unstable poles together with their spatial properties, in ways dependent upon the command input signals.

Limitations on maximal tracking accuracy. 2. Tracking sinusoidal and ramp signals

A novel azimuth velocity estimation method is proposed based on the multiple azimuth squint angles (MASA) imaging mode, acquiring sequential synthetic aperture radar images with different squint angles and time lags. The MASA mode acquisition geometry is given first, and the effect of target motion on azimuth offset and slant range offset is discussed in detail. Then, the azimuth velocity estimation accuracy is analyzed, considering the errors caused by registration, defocusing, and range velocity. Moreover, the interaction between target azimuth velocity and range velocity is studied for a better understanding of the azimuth velocity estimation error caused by the range velocity. With the proposed error compensation step, the new method can achieve a very high accuracy in azimuth velocity estimation, as verified by experimental results based on both simulated data and the TerraSAR-X data.

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Jie Chen

Papers

2-D Coherent Integration Processing and Detecting of Aircrafts Using GNSS-Based Passive Radar

High-Order Analysis Of Critical Stability Properties of Linear Time-Delay Systems

Fixed-time stabilization of linear delay systems by smooth periodic delayed feedback

Limitations on maximal tracking accuracy. 2. Tracking sinusoidal and ramp signals

Moving Target Azimuth Velocity Estimation for the MASA Mode Based on Sequential SAR Images