Silviu-Iulian Niculescu

Static output feedback stabilization: necessary conditions for multiple delay controllers

This note focuses on the static output feedback stabilization problem for a class of single-input-single-output systems when the control law includes multiple (distinct) delays. We are interested in giving necessary conditions for the existence of such stabilizing controllers. Illustrative examples (second-order system, chain of integrators, or chain of oscillators) are presented, and discussed.

Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach, Second Edition

Preface to the second edition Preface to the first edition List of symbols Acronyms Part I. Stability Analysis of Linear Time-Delay Systems 1. Spectral properties of linear time-delay systems 2. Computation of characteristic roots 3. Pseudospectra and robust stability analysis 4. Computation of H2 and H norms 5. Computation of stability regions in parameter spaces 6. Stability regions in delay-parameter spaces Part II. Stabilization and Robust Fixed-Order Control: 7. Stabilization using a direct eigenvalue optimization approach 8. Stabilizability with delayed feedback: a numerical case study 9. Optimization of H norms Part III. Applications: 10. Output feedback stabilization using delays as control parameters 11. Smith predictor for stable systems: delay sensitivity analysis 12. Controlling unstable systems using finite spectrum assignment 13. Congestion control algorithms in networks 14. Consensus problems with distributed delays, with traffic flow applications 15. Synchronization of delay-coupled oscillators 16. Stability analysis of delay models in biosciences Appendix Bibliography Index.

Stability analysis of some classes of TCP/AQM networks

The local stability analysis of some classes of non-linear time-delay systems, encountered as fluid flow models for Transmission Control Protocol/Active Queue Management (TCP/AQM) networks, is addressed. Necessary and sufficient conditions for the asymptotic stability of the linearized models are obtained. Non-linear stability conditions are derived using a Lyapunov–Krasovskii functional approach. An illustrative example completes the paper.

STABILITY ANALYSIS OF A FLUID FLOW MODEL FOR TCP LIKE BEHAVIOR

This note focuses on the stability analysis of some classes of nonlinear time-delay models, encountered as fluid models for TCP/AQM network. By combining analytical and numerical tools, the attractors of these models, as well as the local and global behaviors of the solutions are studied. Among others, the presence of a chaotic attractor is shown, which supports the proposition that TCP itself as a deterministic process can cause or contribute to chaotic behavior in a network. The main goals of the paper are firstly to provide qualitative and quantitative information on the dynamics of the models under consideration, and secondly to illustrate the capabilities of computational tools for stability and bifurcation analysis of delay differential equations to analyze fluid flow models.

Mathematical and Computational Tools for the Stability Analysis of Time-Varying Delay Systems and Applications in Mechanical Engineering

An overview of eigenvalue based tools for the stability analysis of linear periodic systems with delays is presented. It is assumed that both the system matrices and the delays are periodically varying. First the situation is considered where the time-variation of the periodic terms is fast compared to the system’s dynamics. Then averaging techniques are used to relate the stability properties of the time-varying system with these of a time-invariant one, which opens the possibility to use frequency domain tools. As a special characteristic the averaged system exhibits distributed delays if the delays in the original system are time-varying. Both analytic and numerical tools for the stability analysis of the averaged system are discussed. Special attention is paid to the characterization of situations where a variation of a delay has a stabilizing effect. Second, the assumption underlying the averaging approach is dropped. It is described how exact stability information of the original, periodic system can be directly computed. The two approaches are briefly compared with respect to generality, applicability and computational efficiency. Finally the results are illustrated by means of two examples from mechanical engineering. The first example concerns a model of a variable speed rotating cutting tool. Based on the developed theory and using the described computational tools, both a theoretical explanation and a quantitative analysis are provided of the beneficial effect of a variation of the machine speed on enhancing stability properties, which was reported in the literature. The second example concerns the stability analysis of an elastic column, subjected to a periodic force.

Some remarks on stabilizing a chain of integrators using multiple delays

This paper addresses the output feedback stabilization problem of a chain of integrators using multiple delays. We prove that either n distinct delays or a proportional+delay compensator with n-1 distinct delays are sufficient to stabilize a chain including n integrators. We present two different approaches, both are constructive and rely on frequency-domain techniques: on a derivative feedback approximation idea, and a pole placement idea, respectively. An illustrative example (triple integrator) is presented.