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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...
Variation paradigm is introduced for stability in terms of asymptotic gain of persistent dwell-time switched time-delay systems. The principle of small-variation small-state is conceived to formulate conditions on ultimate variations between end times of dwell-time switching intervals for convergence in these intervals. Trajectory convergence is then derived using evolutionary data in both retarded...
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...
A delayed predator-prey model with stage structure is investigated. The linear stability of the system is discussed and Hopf bifurcations are established by using the normal form theory and center manifold theorem. Formula determining the direction of bifurcations and the stability of bifurcating periodic solutions are given. Numerical simulations are carried out to illustrate the theoretical results.
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...
In this paper, we propose a decentralized adaptive output-feedback controller for a class of large-scale time-delay nonlinear systems with unknown high-frequency-gain signs. We establish global asymptotic stabilization results, without using Razumikhin Theorem or constructing Lyapunov-Krasovskii functionals. The paper enlarges the class of large-scale nonlinear systems for which global decentralized...
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 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...
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...
In this paper, a three-species symbiosis Lotka-Volterra model with discrete delays is considered. The stability of positive equilibrium and the existence of Hopf bifurcations are investigated firstly and then the direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem.
As an important tool to study practical problems of biology, engineering and image processing, the cellular neural networks (CNNs) has caused more and more attention. Some interesting results about the existence of solution for cellular neural networks have been obtained. In this paper, by means of iterative analysis, the existence of periodic solution and the uniform stability of the equilibrium...
As an important tool to study practical problems of biology, engineering and image processing, the neural networks has caused more and more attention. Some interesting results on the stability have been obtained. In this paper, the exponential stability of the equilibrium point of a group of Cohen-Grossberg neural networks is obtained by using Lyapunov method and Razumikhin technique.
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