Stabilizing a chain of integrators using multiple delays

This note addresses the output feedback stabilization problem of a chain of integrators using multiple delays. We shall 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.     

Robust stabilization for uncertain time-delay systems containingsaturating actuators

A class of uncertain time-delay systems containing a saturating actuator is considered. These systems are characterized by delayed state equations (including a saturating actuator) with norm-bounded parameter uncertainty (possibly time varying) in the state and input matrices. The delay is assumed to be constant bounded but unknown. Using a Razumikhin approach for the stability of functional differential equations, upper bounds on the time delay are given such that the considered uncertain system is robustly stabilizable, in the case of constrained input, via memoryless state feedback control laws. These bounds are given in terms of solutions of appropriate finite dimensional Riccati equations     

Performance Optimizations for Deploying VoIP Services in Mesh Networks

In the recent past, there has been a tremendous increase in the popularity of VoIP services as a result of huge growth in broadband access. The same voice-over-Internet protocol (VoIP) service poses new challenges when deployed over a wireless mesh network, while enabling users to make voice calls using WiFi phones. Packet losses and delay due to interference in a multiple-hop mesh network with limited capacity can significantly degrade the end-to-end VoIP call quality. In this work, we discuss the basic requirements for efficient deployment of VoIP services over a mesh network. We present and evaluate practical optimizing techniques that can enhance the network capacity, maintain the VoIP quality and handle user mobility efficiently. Extensive experiments conducted on a real testbed and ns-2 provide insights into the performance issues and demonstrate the level of improvement that can be obtained by the proposed techniques. Specifically, we find that packet aggregation along with header compression can increase the number of supported VoIP calls in a multihop network by 2-3 times. The proposed fast path switching is highly effective in maintaining the VoIP quality. Our fast handoff scheme achieves almost negligible disruption during calls to roaming clients     

Robustness assessment via stability radii in delay parameters

This paper focuses on the robust stability analysis of a class of linear systems including multiple delays subjected to constant or time‐varying perturbations. The approach considered makes use of appropriate stability radius concepts (dynamic, static) and relies on a feedback interconnection interpretation of the uncertain system. Various computable bounds on stability radii are obtained that exploit the structure of the problem. Systems including perturbations on both system matrices and delays are also dealt with. Copyright © 2008 John Wiley & Sons, Ltd.     

An adaptive Smith-controller for time-delay systems with relative degree n2

This paper addresses the control of time-delay systems whose relative degree does not exceed two. An adaptive Smith controller together with an adaptive law similar to the delay-free case is proposed. By using Lyapunov–Krasovskii functionals for an appropriate model transformation of the original system, semiglobal stability of the closed-loop system and asymptotic convergence of the output error is established. Strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties. Robustness properties of the adaptive controller are briefly discussed.     

On the stability of linear systems with uncertain delay

This paper focuses on the stability of some class of delay systems, including uncertainty in the delays. More precisely, we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system. If the delay perturbation is constant, necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some (finite-dimensional) constant matrix pencil. If the delay perturbation is time-varying, some sufficient stability conditions are derived using "exact" Lyapunov-Krasovskii functionals. Illustrative examples are also included.     

Cyclic invariance for discrete time-delay systems

This technical communique introduces a new concept of set invariance with respect to linear discrete time dynamics affected by delay. We are interested in the definition and characterization of sequences of cyclically invariant subsets in the state space. The algebraic conditions established in the late ’80s for linear dynamics are generalized to invariance analysis in the presence of delays for given sequences of polyhedral sets.     

Cost-efficient parallel programs based on set-distributions for polynomial interpolation

The paper presents parallel algorithms for Lagrange and Hermite interpolation methods formally derived from specifications, and using set-distributions. Set-distributions are based on set-valued mappings, and they assign a data object to more than one process. The derivation from specifications assures the correctness, and the set-distributions assure the efficiency of the programs. The obtained parallel algorithms have very good time complexities and speeds-up, and they are also cost-efficient. We consider the number of processes p to be a parameter of the algorithms, so, bounded parallelism is considered. The derivation of the algorithms is not ruled by any particular interconnection network. The possible mappings on different networks could be evaluated. The performance analysis is done considering a full-connected network, and other two interconnection networks: hypercube and multi-mesh hypercube, which preserve the cost-efficiency of the algorithms.     

Computing non-fragile PI controllers for delay models of TCP/AQM networks

This article focuses on the stabilisation problem of fluid-flow delay models of transmission control protocol/active queue management (TCP/AQM) networks by using a proportional-integral (PI) controller as AQM strategy. More precisely, the complete set of PI controllers that exponentially stabilises the corresponding linear time-delay system is derived. Using the particular geometric properties of this set of the controller parameters, the issues of robustness to uncertainty in the network parameters and to perturbation in the controller coefficients are addressed. Then, a methodology to compute a non-fragile PI AQM controller is provided. Finally, exponential estimates for the closed-loop system solutions, allowing to evaluate the performance of the corresponding PI-controlled closed-loop system, are proposed by using a Lyapunov–Krasovskii functional approach. An illustrative example completes the presentation.     

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.