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This paper studies the leader-following event-triggered consensus of multi-agent systems with nonlinear dynamics and semi-Markov jump. The information on transition rates is incompletely known. First, by applying weighted orthogonal polynomials, two new integral inequalities are established, which include some existing ones. Second, an event-triggered scheme is presented to save the precious communication resources. After constructing an augmented Lyapunov–Krasovskii functional, a few sufficient conditions are derived to achieve the leader-following event-triggered consensus by utilizing the presented inequalities to manipulate the derivative of the functional. Finally, numerical simulation shows the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The problem of globally exponential stability of static neural networks is investigated. Based on the Lyapunov-Krasovskii functional approach, the free-weighting matrix method, and the Jensen integral inequality, new delay-dependent stability criteria of the unique equilibrium of static neural networks with time-varying delays are presented in terms of linear matrix inequalities (LMIs). The stability criteria can easily be checked by using recently developed algorithms in solving LMIs. A numerical example is given to illustrate the effectiveness and less conservativeness of our proposed method. Index Terms--Globally exponential stability, Jensen integral inequality, linear matrix inequality (LMI), static neural networks, time-varying delays.

The problem ensuring the global exponential stability (GES) of a class of delayed cellular neural networks (CNNs) with time-varying delays is studied. Without assuming the boundedness of the activation functions, by applying the idea of the Lyapunov function, the linear matrix inequality (LMI) techniques, the free-weighting matrix method, and a novel equation, a new sufficient condition for the GES of CNNs with time-varying delays is obtained, which generalizes the previous results in the literature. The criterion is easy to be verified since it takes the form of an LMI. Three numerical examples are given to illustrate the effectiveness and less conservativeness of our proposed method. Index Terms--Cellular neural networks (CNNs), global exponential stability (GES), linear matrix inequality (LMI), time-varying delays.

Generalized homogeneous multivariate matrix Pade-type approximants (GHMPTA) and Pade approximants are studied in ways similar to those of Brezinski and Kida in the scalar cases. By choosing an arbitrary monic bivariate scalar polynomial from the triangular form as the generating one of the approximant, we discuss their several typical important properties and study the connection between generalized homogeneous bivariate matrix Pade-type approximants and Pade approximants. The arguments given in detail in two variables can be extended directly to the case of d variables (d [greater than or equal to] 2). Index Terms--Covariance matrix, multivarianl analysis, polynomial approximation, polynomials.