Yi S., Nelson P.W., Ulsoy A.G. Time-Delay Systems: Analysis and Control Using the Lambert W Function

Singapore: World Scientific Publishing Company, 2010. - 153p.This book comprehensively presents a recently developed novel methodology for analysis and control of time-delay systems. Time-delays frequently occurs in engineering and science. Such time-delays can cause problems (e.g. instability) and limit the achievable performance of control systems. The concise and self-contained volume uses the Lambert W function to obtain solutions to time-delay systems represented by delay differential equations. Subsequently, the solutions are used to analyze essential system properties and to design controllers precisely and effectively.Motivation
Delay differential equation
Lambert W function
Scope of This Document
Original ContributionsGeneralization to free systems of DDEs
Stability
Forced Systems
Generalization to systems of DDEs
Approach Using the Laplace Transformation
Scalar case
Generalization to systems of DDEs
Concluding RemarksThe Chatter Equation in the Turning Process
Solving DDEs and Stability
Eigenvalues and stability
Concluding RemarksControllability
Observability
Illustrative Example
Conclusions and Future WorkEigenvalue assignment
Scalar case
Systems with control delays
Systems with state delays
ConclusionsStability radius
Design of robust feedback controller
Time-Domain Specifications
Concluding RemarksProblem Formulation
Controllability, observability, and eigenvalue assignability
Design of Observer-Based Feedback Controller
Separation principle
Application to Diesel Engine Control
ConclusionsHIV Pathogenesis Dynamic Model with an Intracellular Delay
Delay effects on rightmost eigenvalues
Mutation, drug efficacy and eigenvalues
HIV: Eigenvalue sensitivity
Eigenvalue sensitivity and response sensitivity
Concluding Remarks and Future WorkCommutation of Matrices A and S in Eq. (2.10)
Reduction of Eqs. (2.31) and (2.32) to Eq. (2.36)
Proof Regarding Minimal Energy
Comparisons with Other Types of Controllability and Observability
C Limits in Assignment of Eigenvalues