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

Ionospheric effect is considered to be one of the factors limiting the accuracy of deformation measurement acquired from interferometric SAR data. The correction of this error source was studied recently, and some new methods was developed and improved. One of these methods is the range Split-Spectrum. In this work, we introduce a new algorithm for implementing the method. An improvement is made, when one corregistration step is performed, and no resampling of the slave images is needed. The performance of the method is studied on a couple of ALOS data, the variation of the differential STEC on the interferogram, was determined as less than 0.5 TECU.

A Refined Split-Spectrum algorithm for correcting ionospheric effects on interferograms of spaceborne D-InSAR at longer wavelength

Fundamental Bounds for Stabilizability of Continuous-Time Systems under Stochastic Multiplicative Uncertainty and Delay*

This paper studies an optimal control problem which is to minimize jointly the error in tracking a step reference and the energy of the plant input. We derive an analytical expression for the best attainable performance. It is found that this performance depends not only on the plant nonminimum phase zeros-a fact known previously-but also on the plant gain in the entire frequency range. The result thus reveals and quantifies another source of fundamental performance limitations beyond those already known, which are nonexistent when only conventional performance objectives such as tracking and regulation are addressed individually. It shows, among other observations, that the bandwidth as well as minimum phase zeros of the plant may all impose constraints on the achievable performance.

Tracking performance with finite input energy

In this paper, we study a modified Kalman filter (MKF) over networks admitted multi-channel packet drops and investigate the existence of a stabilizing solution to the corresponding modified algebraic Riccati equation (MARE). Random multi-channel packet drops, compared with other previous formulations, are allowed to be correlated in spatial in this contribution. We first derive two different necessary and sufficient conditions to ensure mean-square detectability of the considered system in operator- and time-domain respectively. Then, including the necessity of the mean-square detectability, an explicit necessary and sufficient condition to the existence of a stabilizing solution to the MARE is derived, which can perfectly reduce to the existence condition to standard algebraic Riccati equation (ARE) whenever the absent of packet drops. Meanwhile, the stabilizing solution can be obtained by solving a set of linear matrix inequalities (LMIs).

Kalman Filtering over Networks in Presence of Multi-Channel Correlated Packet Drops

We consider the Cauchy problem for the complex valued semi-linear heat equation $$\begin{aligned} \partial _t u - \Delta u - u^m =0, \ \ u (0,x) = u_0(x), \end{aligned}$$ where $$m\ge 2$$ is an integer and the initial data belong to super-critical spaces $$E^s_\sigma $$ for which the norms are defined by $$\begin{aligned} \Vert f\Vert _{E^s_\sigma } = \Vert \langle \xi \rangle ^\sigma 2^{s|\xi |}\widehat{f}(\xi )\Vert _{L^2}, \ \ \sigma \in \mathbb {R}, \ s<0. \end{aligned}$$ If $$s<0$$ , then any Sobolev space $$H^{r}$$ is a subspace of $$E^s_\sigma $$ , i.e., $$\cup _{r \in \mathbb {R}} H^r \subset E^s_\sigma $$ . We obtain the global existence and uniqueness of the solutions if the initial data belong to $$E^s_\sigma $$ ( $$s<0, \ \sigma \ge d/2-2/(m-1)$$ ) and their Fourier transforms are supported in the first octant, the smallness conditions on the initial data in $$E^s_\sigma $$ are not required for the global solutions. Moreover, we show that the error between the solution u and the iteration solution $$u^{(j)}$$ is $$C^j/(j\,!)^2$$ . Similar results also hold if the nonlinearity $$u^m$$ is replaced by an exponential function $$e^u-1$$ . 

Jie Chen

Papers

A Refined Split-Spectrum algorithm for correcting ionospheric effects on interferograms of spaceborne D-InSAR at longer wavelength

Fundamental Bounds for Stabilizability of Continuous-Time Systems under Stochastic Multiplicative Uncertainty and Delay*

Tracking performance with finite input energy

Kalman Filtering over Networks in Presence of Multi-Channel Correlated Packet Drops

Complex valued semi-linear heat equations in super-critical spaces $$E^s_\sigma $$