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

/pdf/stability-of-time-delay-systems-5d2qjgdknf.pdf

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

/pdf/a-survey-of-recent-results-in-networked-control-systems-2vqnhq8czm.pdf

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.

/pdf/essentials-of-robust-control-3kaks6yk3h.pdf

Essentials of Robust Control

In this paper we study the robust stability independent of delay of some class of uncertain quasipolynomials, whose coefficients may vary in a certain prescribed range. Our main contributions include frequency-sweeping conditions for interval, diamond and spherical quasipolynomial families. The corresponding results provide necessary and sufficient conditions, and are easy to check, requiring only the computation of two simple frequency-dependent functions.

Robust stability of quasipolynomials: frequency-sweeping conditions

In this paper we study delay robustness of PID controllers in stabilizing systems containing uncertain delays. We consider second-order systems and seek analytical characterization and exact computation of the PID delay margin, where by PID delay margin we mean the maximal range of delay values within which the system can be robustly stabilized by a PID controller. Our primary contribution is threefold. First, we show that under a nonrestrictive assumption, the delay margin achieved by PID control coincides with that by PD controllers. Second, we show that the PID delay margin can be computed efficiently by solving a pseudo-concave unimodal problem, that is, a univariate optimization problem that admits a unique maximum and hence is a convex optimization problem in one variable. As such, from a computational standpoint, the PID delay margin problem can be considered resolved. Finally, we demonstrate analytically the trade-off between achieving delay margin and tracking performance, showing that for several canonical performance criteria, integral control reduces the delay margin. These results not only ensure that the PID delay margin problem be readily solvable, b

Delay Robustness of PID Control of Second-Order Systems: Pseudo-Concavity, Exact Delay Margin, and Performance Trade-Off

This paper addresses the problem of asymptotic stability of linear time-delay systems with commensurate delays. We study the asymptotic behavior of the critical characteristic zeros of such 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 consider time-delay systems given in both state-space form and as a quasipolynomial. Our results reveal that in the former case the zero asymptotic behavior can be characterized by solving a simple eigenvalue problem, and in the latter case, by computing the derivatives of the quasipolynomial. To perform such an analysis, we make use of an operator perturbation approach.

/pdf/asymptotic-behavior-of-imaginary-zeros-of-linear-systems-4cyqg2kaqj.pdf

Asymptotic Behavior of Imaginary Zeros of Linear Systems with Commensurate Delays

In this paper we study delay robustness of PID controllers in stabilizing systems containing uncertain, variable delays. We consider second-order unstable systems and seek analytical characterization and exact computation of the PID delay margin, where by PID delay margin we mean the maximal range of delay values within which the system can be robustly stabilized by a PID controller. Our contribution is threefold. First, we show that the delay margin achieved by PID control coincides with that by PD controllers. Second, we show that other than helping stabilize the delay-free part of a plant, the proportional control contributes no action to increase the delay margin. Finally, we show that the PID delay margin can be computed efficiently by solving a unimodal problem, that is, a univariate optimization problem that admits a unique maximum and hence is a convex optimization problem in one variable. This unimodal problem is one of pseudo-concave optimization and hence can be solved using standard convex optimization or gradient-based methods. As such, from a computational perspective, the PID delay margin problem is completely resolved in this paper! The results not only insure that the PID delay margin problem be readily solvable, but also provide fundamental conceptual insights into the PID control of delay systems, and analytical justifications to long-held engineering intuitions and heuristics, thus lending useful guidelines in the tuning and analytical design of PID controllers.

Exact Computation of Delay Margin by PID Control: It Suffices to Solve a Unimodal Problem!

* Part I: Robust and Optimal Control * Chapter 1: Measurement-based control design for unknown systems * Chapter 2: Quantized linear quadratic Gaussian control for scalar systems * Chapter 3: Robust Hinfinity filter design for nonuniformly sampled systems * Chapter 4: Analysis of frequency response across switching * Chapter 5: Optimal tracking and power allocation over AWN feedback channels * Chapter 6: Stability analysis for a class of Hamiltonian systems with digital control * Part II: Mathematical System and Control Theory * Chapter 7: Maximizing mutual information between random variables and applications to order reduction of stochastic processes * Chapter 8: On compact sets in the graph topology * Chapter 9: Matrix pencils in time and frequency domain system identification * Chapter 10: Identification of nonparametric piecewise affine models via data compression * Chapter 11: Performance benefits in two-axle railway vehicle suspensions employing inerters * Chapter 12: Stabilization of quantum spin systems via continuous feedback control * Part III: Networked Dynamical Systems and Glocal Control * Chapter 13: Combining distance-based formation shape control with formation translation * Chapter 14: Energy management in wireless sensor networks * Chapter 15: Distributed randomized PageRank algorithms over unreliable channels * Chapter 16: Stabilization of multi-input networked control systems over additive white Gaussian noise channels * Chapter 17: Clustering of large-scale dynamical networks for glocal control * Chapter 18: Glocal control for natural oscillations

Jie Chen

Papers

Robust stability of quasipolynomials: frequency-sweeping conditions

Delay Robustness of PID Control of Second-Order Systems: Pseudo-Concavity, Exact Delay Margin, and Performance Trade-Off

Asymptotic Behavior of Imaginary Zeros of Linear Systems with Commensurate Delays

Exact Computation of Delay Margin by PID Control: It Suffices to Solve a Unimodal Problem!

Developments in Control Theory Towards Glocal Control