Event-Based Time-Interval Pinning Control for Complex Networks on Time Scales and Applications
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This paper studies the synchronization problem for linear complex dynamical networks (CDNs) on time scales. An intermittent dynamic time-interval pinning control strategy is designed to achieve synchronization for CDNs with the isolated node. Based on the Lyapunov approach and the theory of time scales, synchronization criteria are established for CDNs on general time scales. The main results in the paper show that, by controlling a proportion of the network nodes, the exponential synchronization can be achieved. Moreover, the infinitely fast switching of the pinning node set is avoided by means of the event-triggered strategy. According to our selection algorithm, the number of pinning nodes will be updated online at each pinning time. The modeling framework investigated in this paper is a unification and generalization of many existing continuous-time and discrete-time complex network models. Three numerical examples are given to illustrate the effectiveness and priority of the obtained results. Finally, the analytical results are applied to the distributed auxiliary control of microgrids and formation control of spacecraft.Keywords:
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In this paper, switched linear systems are considered and dwell and average dwell time for their global asymptotic stability is examined. Dwell and average dwell time are determined based on the condition number for the global asymptotic stability of switched linear differential systems. Numerical examples which show the effect of the results obtained are given with the new dwell and average dwell times.
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This paper studies the stability of switched Cohen-Grossberg neural networks with interval time-varying delay and distributed time-varying delay. A piecewise Lyapunov function is utilized to deal with the switching problems of stability. The switching signals are arbitrary under the constraint of the average dwell time which is calculated by collecting the state decay estimation of subsystem. Sufficient conditions are obtained in terms of linear matrix inequality (LMI) to guarantee the exponential stability for the switched Cohen-Grossberg neural networks. Numerical example is provided to illustrate the effectiveness of the proposed method.
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Abstract This paper considers the stabilization problem for a class of switched systems with state constraints based on mode‐dependent average dwell time (MDADT) in discrete‐time context. An improved average dwell time method is proposed, which is less conservative than the common average dwell time method. The sufficient conditions and stabilizing state feedback controllers for stabilization of discrete‐time switched systems with state constraints under MDADT switching are derived. Finally, the simulation results show that the approach designed by this paper is effective.
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This paper addresses the filtering problem for a class of discrete-time switched linear parameter varying systems under average dwell time switching. The stability result for general discrete-time switched systems with average dwell time is first presented. A mode-dependent full-order parameterized filter is then designed and the corresponding existence conditions of such filters are derived via LMI formulation. The desired filter gains and the admissible switching signals are obtained for a given system decay degree such that the resulting filter error system is exponentially stable and has a guaranteed H ∞ performance. A numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results.
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This paper addresses the exponential admissibility of a class of discrete-time switched singular systems with time-varying delay. By defining a properly constructed decay-rate-dependent Lyapunov function and using the average dwell time approach, a delay-dependent sufficient condition is derived for the system to be regular, causal and exponentially stable. The obtained results provide a solution to one of the basic problems in discrete-time switched singular time-delay systems, that is, to identify a switching signal for which the switched singular time-delay system is regular, causal and exponentially stable. Numerical example is given to demonstrate the effectiveness of the proposed results.
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