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The Vivaldi algorithm is known to be one of the most interesting approaches for the calculation of Internet coordinates. It is a fully distributed, light-weight and adaptive algorithm. Recent studies show that host coordinates in the Vivaldi system are not stable and are drifting rapidly even when the network delays do not change. In this paper we observe that, despite the instability of Vivaldi coordinates...
This paper proposes a novel stability analysis of linear systems with sampled-data inputs. Inspired by the input-delay approach and the stability of impulsive systems, this method provides novel sufficient stability conditions. The stability analysis concerns both constant and time-varying sampling periods. The delay-dependent conditions are expressed using computable linear matrix inequalities. Several...
For LTI systems with a time-varying input delay, an explicit formula for predictor feedback was presented by Nihtila in 1991. In this note we construct a time-varying Lyapunov functional for the closed-loop system and establish exponential stability. The key challenge is the selection of a state for a transport PDE, which has a non-constant propagation speed, and which is the basis of the stability...
We present an approach for compensating input delay of arbitrary length in nonlinear control systems. This approach, which due to the infinite dimensionality of the actuator dynamics and due to the nonlinear character of the plant results in a nonlinear feedback operator, is essentially a nonlinear version of the Smith Predictor and its various predictor-based modifications for linear plants. Global...
This paper considers interval time-varying delay systems with delayed estimation of the delay. This case is often encountered in the Networked Control Systems (NCS) field. Based on Lyapunov-Krasovskii functional methods and linear matrix inequality (LMI) techniques, a switching state feedback controller is designed to guarantee the exponential stability. The controller switches according to the measured...
This paper is concerned with the stochastic stabilizability problem of time-delayed Markovian jump bilinear systems with saturating actuators. Based on the reduction method, sufficient conditions are proposed to guarantee local exponential stochastic stability of the closed-loop systems with delayed feedback control. A numerical example is provided to demonstrate the effectiveness of the proposed...
A Smith Predictor-like design for compensation of arbitrarily long input delays is available for general, controllable, possibly unstable LTI finite-dimensional systems. Such a design has not been proposed previously for problems where the plant is a PDE. We present a design and stability analysis for a prototype problem, where the plant is a reaction-diffusion (parabolic) PDE, with boundary control...
This paper deals with stabilization of networked control systems (NCS) affected by uncertain time-varying delays and data packet dropouts. We point out that such network effects are likely to render the classical control Lyapunov function (CLF) method unfeasible, mainly due to the monotonic decreasing condition. To solve this problem we make use of a discrete-time equivalent of a control Lyapunov-Razumikhin...
Stability conditions for state-delay systems are derived based on the norm of semigroup, which describes the transition of the internal state. Introducing an exact calculation method of the semigroup norm, the conditions for the internal stability and the marginal stability are characterized by non-singularity of a transcendental function. The conditions depend on the existence of time interval such...
This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain theorem for operators is examined. The result developed for operators allows applications to a wide class of systems, including state space systems with delays.
We show that for a general class of distributed power control algorithms in wireless networks, if a feasible steady state power allocation exists, this is asymptotically stable for arbitrary gains and time varying heterogeneous delays. The analysis exploits certain contraction properties of the interference in such algorithms, and makes use of Lyapunov Razumikhin functions to address the infinite...
This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain...
By taking advantage of the packet-based transmission in networked control systems (NCSs), a packet-based control approach is proposed for NCSs. Using this approach, the control law can be designed with explicit compensation for network-induced delay, data packet dropout and data packet disorder simultaneously. The sufficient and necessary condition for the stochastic stability of the closed-loop system...
We study global stabilization of strict-feedforward systems with arbitrarily long input delay. These systems may be open-loop unstable but cannot exhibit finite escape instability, providing for a possibility of global stabilization even in the presence of long delay. We derive predictor-based feedback laws for exact compensation of input delay. These feedbacks are given explicitly due to the fact...
In the presence of long input delay, global stabilization is possible for all nonlinear systems that are forward complete. Within this class, globally stabilizing feedback laws can be derived explicitly for systems within the class of strict-feedforward systems. These results are contained in companion papers of the present paper. In the present paper we focus on the feedback linearizable subclass...
This paper studies the stabilization problem for a class of networked control systems (NCSs) with communication constraints and random packet dropouts. The considered plant is equipped with multiple sensor nodes and actuator nodes. Only one of them can communicate with the controller at each transmission instant due to the communication constraints, and packet dropouts may occur at each transmission...
Smith Predictor-like designs for compensation of arbitrarily long input delays are commonly available only for finite-dimensional systems. Only very few examples exist where such compensation has been achieved for PDE systems, including our recent result for a parabolic (reaction-diffusion) PDE. In this paper we address a more challenging wave PDE problem, where the difficulty is amplified by allowing...
This paper addresses the H?? stability analysis of neutral time-delay systems with multiple commensurate delays including those with poles asymptotic to the imaginary axis. This extends previous work where only the single delay case was considered. Some frequency-domain tests for this kind of stability are proposed.
This paper presents a new stability analysis of linear networked control systems. The new method is inspired by discontinuous Lyapunov functions that were introduced by using impulsive system representation of the sampled-data and of the networked control systems respectively. In the recent paper piecewise-continuous (in time) Lyapunov-Krasovskii functionals have been suggested for the stability analysis...
Due to the rapid spreading nature of Internet worms, it is necessary to implement automatic mitigation on the Internet. Inspired by worm vaccinations, we propose a novel epidemic model which combines both vaccinations and dynamic quarantine methods, referred to as SEIQV model. Using SEIQV model, we obtain the basic reproduction number that governs whether or not a worm is extinct. The impact of different...
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