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 paper studies the tracking performance of sampled-data control systems. We consider the problem of tracking a step reference input by a sampled-data controller, and the goal is to minimize the integral square of the error between the output and input signals. Under this criterion, of particular interest is to investigate whether and when a degradation in the tracking performance may result, due to the use of sampled-data controllers, and whether such a degradation, where it does exist, can be remedied by a sufficiently fast sampler. The degradation thus constitutes a gap between the optimal performance achievable by continuous-time controllers and that by optimal sampled-data controllers. It is shown that for plants with relative degree greater than one, a performance loss does take place and it can never be recovered despite that the sampler is allowed to operate arbitrarily fast. This performance loss is seen to be fundamental of the sampling and hold mechanism, rather than from the plant itself. It is also shown that for plants with relative degree one, the loss can indeed. be retrieved with a sufficiently fast sampler.

Asymptotic tracking performance of sampled-data systems

In this paper we study the fundamental limitations in stabilization and tracking of multi-input, multi-output (MIMO) networked feedback systems. We adopt a parallel additive white noise (AWN) model for the MIMO communication channel, and consider as our performance measure the mean square error for a system's output to track a random reference signal with finite power. Of particular interest in our study is the joint design of the controller and the channel to mitigate the requirement on feedback stabilization and to better the tracking performance. To this effect we consider scaled AWN channels, with positive diagonal scaling matrices interpreted as static coders and decoders. By casting the problem as a constrained optimal H 2 control problem and employing duality principles, we derive necessary and sufficient conditions for the system to be mean-square stabilizable and analytical characterizations for the best achievable performance under channel input power constraint. While fundamental limits are known to exist, it is seen that an appropriate channel scaling can be employed to exploit the channel power effectively so as to fundamentally improve a system's stabilizability and tracking performance.

Optimal tracking by LTI controllers over scaled MIMO additive white noise channels

A mixed deterministic/probabilistic model validation problem is investigated in this technical note, which consists in an additive uncertain model with model uncertainty characterized by the H∞ norm. The data available for validation are time-domain experimental data corrupted by a random noise sequence. Our aim is to compute the probability for such an uncertain model to be validated by the data, and our main results are bounds on this probability that are computable based on the distribution of Chi-square random variables when the noise is a Gaussian variable, and solvable as an LMI problem when only statistical information such as the expectation and covariance of the noise are known.

Probabilistic Estimates for Mixed Model Validation Problems With ${\cal H}_{\infty}$ Type Uncertainties

Synthetic Aperture Radar (SAR) is widely used in remote sensing field, especially for the acquisition of quantitative information about the earth’s environment. Calibration processing is critical for SAR image quantitative applications. This paper proposes a spaceborne SAR calibration simulator to describe the calibration process. First, Amazon rainforest area SAR image from Gaofen-3 was chosen to generate backscatter coefficient by adding a reference reflector for the purpose of quantitative analysis. Then the backscatter coefficient was entered into the spaceborne SAR calibration simulator. The simulator will perform echo simulation based on the system parameters of Gaofen-3. Based on the simulation echo, image formation processing is implemented for generating the focusing image. Furthermore, peak method and integral method were utilized to calibrate the SAR image. Simulation results show that integral method is better for calibration accuracy.

A Spaceborne SAR Calibration Simulator Based on Gaofen-3 Data

The purpose of this paper is to present an extension to some of the current work on worst-case identification problems to multivariable systems. We consider an H/sub /spl infin// identification problem for a class of linear shift invariant multi-input multi-output systems. Our main results are an interpolatory algorithm and a number of bounds on identification error. This algorithm operates on available input and output data in the time domain, and is constructed by solving an extended matrix tangential Caratheodory-Fejer problem. Similar to its counterpart for scalar systems, this interpolatory algorithm possesses certain desirable optimality properties and can be obtained via standard convex programming methods. >

Jie Chen

Papers

Asymptotic tracking performance of sampled-data systems

Optimal tracking by LTI controllers over scaled MIMO additive white noise channels

Probabilistic Estimates for Mixed Model Validation Problems With ${\cal H}_{\infty}$ Type Uncertainties

A Spaceborne SAR Calibration Simulator Based on Gaofen-3 Data

H/sub /spl infin// identification of multivariable systems by tangential interpolation methods