A new sufficient conditions for the global exponential stability of the equilibrium point for delayed cellular neural networks （DCNNs） is presented. It is shown that the use of a more general type of Lyapunov-Krasovskii function enables the derivation of new results for an exponential stability of the equilibrium point for DCNNs. The results establish a relation between the delay time and the parameters of the network. The results are also compared with one of the most recent results derived in the literature.
To investigate the leader-following formation control, in this paper we present the design problem of control protocols and distributed observers under which the agents can achieve and maintain the desired formation from any initial states, while the velocity converges to that of the virtual leader whose velocity cannot be measured by agents in real time. The two cases of switching topologies without communication delay and fixed topology with time-varying communication delay are both considered for multi-agent networks. By using the Lyapunov stability theory, the issue of stability is analysed for multi-agent systems with switching topologies. Then, by considering the time-varying communication delay, the sufficient condition is proposed for the multi-agent systems with fixed topology. Finally, two numerical examples are given to illustrate the effectiveness of the proposed leader-following formation control protocols.
A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.
This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.
Yumei LIXinping GUANDan PENGChangchun HUAXiaoyuan LUO
This paper researched into some methods for generating min-weighted rigid graphs and min-weighted persistent graphs. Rigidity and persistence are currently used in various studies on coordination and control of autonomous multi-agent formations. To minimize the communication complexity of formations and reduce energy consumption, this paper introduces the rigidity matrix and presents three algorithms for generating rain-weighted rigid and min- weighted persistent graphs. First, the existence of a min-weighted rigid graph is proved by using the rigidity matrix, and algorithm 1 is presented to generate the min-weighted rigid graphs. Second, the algorithm 2 based on the rigidity matrix is presented to direct the edges of min-weighted rigid graphs to generate min-weighted persistent graphs. Third, the formations with range constraints are considered, and algorithm 3 is presented to find whether a framework can form a min-weighted persistent formation. Finally, some simulations are given to show the efficiency of our research.
Recently, a two-dimensional （2-D） Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O（L2） from O（L4）. The effectiveness of the proposed algorithm is illustrated by experimental results.
In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.
