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

Exact computation of maximal allowable delay for general second-order multi-agents consensus

The final value theorem is an extremely handy result in Laplace transform theory. In many cases, such as in the analysis of proportional-integral-derivative (PID) controllers, it is necessary to determine the asymptotic value of a signal. The final value theorem provides an easy-to-use technique for determining this value without having to first invert the Laplace transform to determine the time signal. The standard assumptions for the final value theorem [1, p. 34] require that the Laplace transform have all of its poles either in the open-left-half plane (OLHP) or at the origin, with at most a single pole at the origin. In this case,

Infinite Limits and Irrational Functions

Objective
To explore the influence of signal noise ratio (SNR) on analysis of clear cell renal cell carcinoma (CCRCC) using DWI with multi-b values.


Methods
The images of 17 cases with CCRCC were analyzed, including 17 masses and 9 pure cysts. The signal intensity of the cysts and masses was measured separately on DWI for each b value. The minimal SNR, as the threshold, was recorded when the signal curve manifest as the single exponential line. The SNR of the CCRCC was calculated on DWI for each b value, and compared with the threshold by independent Two-sample t Test.


Results
The signal decreased on DWI with increased b factors for both pure cysts and CCRCC. The threshold is 1.29±0.17, and the signal intensity of the cysts on DWI with multi-b values shown as a single exponential line when b≤800 s/mm2. For the CCRCC, the SNR is similar to the threshold when b=1 000 s/mm2 (t=0.40, P=0.69), and is lower when b=1 200 s/mm2 (t=-2.38, P=0.03).


Conclusion
The SNR should be sufficient for quantitative analysis of DWI, and the maximal b value is 1000 s/mm2 for CCRCC.


Key words: 
Magnetic resonance imaging; Diffusion tensor imaging; Clear cell renal cell carcinoma

[Evaluation of signal noise ratio on analysis of clear cell renal cell carcinoma using DWI with multi-b values].

For high resolution spaceborne SAR system, the errors caused by straight trajectory assumption and stop-go approximation cannot be ignored. In this paper, an algorithm is proposed to compensate the above errors. First, a novel modified hyperbolic range equation (MHRE) is introduced to describe the satellite's orbit which is more precise than the traditional hyperbolic range equation (THRE). Then, the accurate signal model without stop-go approximation is deduced based on the MHRE. What's more, the residual phase errors in two-dimensional frequency domain caused by the two error sources are obtained. At last, the accuracy and validity of the proposed compensation algorithm are verified by the computer simulation results.

Accurate compensation of stop-go approximation for high resolution spaceborne SAR using modified hyperbolic range equation

We extend the classical Bode integral relations to multi-input multi-output systems. Our main contributions include Bode and Poisson type integral inequalities for the sensitivity and complementary sensitivity functions, together with bounds on the sensitivity and complementary sensitivity magnitudes, which are obtained for both continuous-time and discrete-time systems. Part I presents Bode type integral inequalities. These inequalities may be viewed as some variants to the previously available results, but are also significantly different. The main difference is two fold. First, while the previous integral equalities are valid only under a restrictive assumption, the results herein hold in general. Secondly, in spite of the fact that the present results are based upon techniques and assumptions similar to those used in deriving Bode type integral inequalities, the in-depth study carried out here leads to more explicable expressions particularly indicative of the adverse effects of open loop unstable poles. As a direct outcome, the new results confirm that in a multivariable system design limitation and tradeoff depends on both the locations and directions of open loop unstable poles, and in particular, in how such directions may be aligned. The latter is characterized by angles measuring the mutual orientation between the pole directions.

Jie Chen

Papers

Exact computation of maximal allowable delay for general second-order multi-agents consensus

Infinite Limits and Irrational Functions

[Evaluation of signal noise ratio on analysis of clear cell renal cell carcinoma using DWI with multi-b values].

Accurate compensation of stop-go approximation for high resolution spaceborne SAR using modified hyperbolic range equation

On logarithmic integrals and performance bounds for MIMO systems. I. Sensitivity integral inequalities