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

In this paper, we study the problem of stabilizability of LTI systems over both the forward (from the controller to the plant) and feedback (from the sensor to the controller) channel. We adopt the additive white noise (AWN) channel with a prescribed power constraint as our channel model. For first order systems, we derive explicitly the necessary and sufficient conditions for stabilizability and show the tradeoff between the minimum signal-to-noise ratio (SNR) required for the forward and feedback channel. We also show explicitly that the use of two-parameter controller in this problem assumes better performance.

Stabilization over additive white noise forward and feedback channels

In this paper we study robust consensus problems for continuous-time first-order multi-agent systems (MAS) connected by an undirected network. We derive analytical expressions of the delay consensus margin achievable by the PID feedback protocols; the delay consensus margin is a robustness measure that defines the maximal range of delay within which robust consensus can be achieved despite the uncertainty in the delay. The results show how the agent dynamics and graph connectivity may fundamentally limit the range of delay tolerable, so that consensus can and cannot be maintained in the presence of uncertainty in the delay. Somewhat surprisingly but yet in an intuitively consistent manner, we find that the delay consensus margin achieved by PID feedback coincides with that by PD protocols, which can be determined by solving efficiently a convex optimization problem in one variable, or alternatively, a unimodal optimization problem.

Exact Delay Consensus Margin of First-Order Agents under PID Protocol

In this chapter, we extend the preceding stabilization results to linear systems with time-varying delays. The extension is rendered possible by the operator-theoretic approaches developed in Chaps. 3 and 4: While the small-gain stability conditions are developed in Chap. 3 for systems with time-varying delays, the interpolation approach used in Chap. 4 enables us to address stabilization problems directly based on the small-gain conditions. This insures that the results on the delay margin can be cohesively extended, and in a unified manner. Indeed, it will be seen that bulk of the results in Chap. 4 can be used to address the stabilization of systems with time-varying delays, modulo to some minor modifications. Efficient computational formulas and analytical expressions are also obtained, which incorporate the time-varying delay characteristics of delay range and delay variation rate.

Stabilization of Linear Systems with Time-Varying Delays

This paper studies sign-consensus of linear multi-agent systems, i.e., states of all agents will eventually have the same sign, but may with different magnitudes. The interactions between agents consist of both collaboration and competition, which is modeled by a signed directed graph. Moreover, the graph is allowed to be structurally unbalanced and time varying. To achieve sign-consensus, condition of the graph topology is obtained, and distributed control law is proposed and analyzed.

Jie Chen

Papers

Stabilization over additive white noise forward and feedback channels

Exact Delay Consensus Margin of First-Order Agents under PID Protocol

Stabilization of Linear Systems with Time-Varying Delays

Sign-consensus of multi-agent systems over fast switching signed graphs

On the Weierstrass Preparation Theorem with Applications to the Asymptotic Analysis of Characteristics Roots of Time-Delay Systems.