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We consider finite volume numerical schemes for stabilizing dynamics governed by scalar nonlinear hyperbolic conservation laws through feedback boundary conditions. Using a discrete Lyapunov function we prove the decay of the discrete solution given by first-order finite volume schemes in conservative form to a desired stationary state up to the order of the time step. Theoretical results are accompanied...
In the paper, we firstly give a new accurate spheroid estimation formula of the globally exponentially attractive set for all positive parameters by constructing a generalized positive definite Lyapunov functions with radially unbound. Secondly, based on inequalities techniques, linear feedback control with one input or two inputs is proposed to realize the globally exponential synchronization of...
This paper treats the globally exponential synchronization problem for a new energy resource chaotic system with two scroll attractors via nonlinear feedback of partial states. Nonlinear feedback rules with some variables and two inputs are derived based on Lyapunov stability theory. The most important features are that the synchronization is achieved through the control of some variables and the...
This paper treats the globally exponential synchronization problem of a new Lorenz-like chaotic systems. Based on Lyapunov stability theory and some inequalities techniques, two control approaches, namely both linear feedback control with one state feedback and one input or with one state feedback and two inputs and nonlinear feedback control with two inputs, are proposed to realize the globally exponential...
This paper treats the globally exponentially attractive set and synchronization problem of a new Lorenz-like chaotic systems. Firstly, based on the definition of globally exponentially attractive set and Lyapunov stability theory, by constructing a family of generalized positive definite Lyapunov functions with radially unbound respect with to the parameters of the system, a new estimation of the...
This paper is devoted to the study of multi-agent consensus with a time-varying reference state in directed networks with both switching topology and time-varying delay. Stability analysis is performed based on a proposed Lyapunov-Krasovskii function. Sufficient conditions based on linear matrix inequalities (LMIs) are given to guarantee multi-agent consensus on a time-vary reference state under arbitrary...
This paper is devoted to the study of multi-agent consensus with a time-varying reference state in directed networks with both switching topology and constant time delay. Stability analysis is performed based on a proposed Lyapunov-Krasovskii function. Sufficient conditions based on linear matrix inequalities (LMIs) are given to guarantee multi-agent consensus on a time-vary reference state under...
This Letter deals with the global exponential synchronization of a class of chaotic networks with time delays. Based on the Halanay inequality technique and the Lyapunov stability theory, the global synchronization of a network about its all variables is derived by only considering the global synchronization of its partial variables, and a delay-independent criteria and decentralized control law is...
This paper treats the chaotic synchronization problem for Rikitake chaotic systems via unidirectional coupling with partial systems states. Two control approaches, namely the self coupling of single state variable and nonlinear feedback controller with partial systems states, are investigated. Based on the Lyapunov stability technique, control laws based on single variable of driven system are derived...
In this study, a novel procedure is presented for control and analysis of multiple autonomous agents with point mass dynamics achieving flocking motion. Two control laws are proposed for a group of autonomous agents to achieve flocking formations related to two different centers (mass center and geometric center) of the flock. The first one is designed for flocking motion based on mass center and...
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