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In this paper, the stability and $L_2$ -gain properties of linear impulsive delay systems with delayed impulses are studied. Commonly employed techniques, in which the delayed impulses are treated using Newton–Leibniz formula, may not be applicable to $L_2$ -gain analysis, since they make the disturbance input appear in the impulse part. In order to circumvent the difficulty, we first augment the considered system to a time-delay system with switching nondelayed impulses. Due to the absence of delayed impulses, this new approach has advantages in constructing Lyapunov functions and handling the effects of impulse delays on the system performance. Switching-based time-dependent Lyapunov functions are introduced to deal with the resultant switching impulses of the augmented system. Sufficient conditions for exponential stability and $L_2$ -gain properties are derived in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach. [ABSTRACT FROM AUTHOR]

In this note, we investigate the stabilization of discrete-time linear systems with an unknown time-varying delay. Existing literature on the stabilization of time-delay systems require some knowledge, such as an upper bound, of the delay. In this paper, by proposing a switched low-gain feedback control law, we are able to achieve asymptotic stabilization of the system without any knowledge of the delay. In addition, the proposed switched low-gain feedback law also significantly improves the closed-loop system performance in terms of overshoot and convergence speed in comparison with the traditional fixed gain design. Simulation study illustrates the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the $p$ th moment input-to-state exponential stability for delayed recurrent neural networks (DRNNs) with Markovian switching is studied. By using stochastic analysis techniques and classical Razumikhin techniques, a generalized vector $ {\mathcal {L}}$ -operator differential inequality including cross item is obtained. Without additional restrictive conditions on the time-varying delay, the sufficient criteria on the $p$ th moment input-to-state exponential stability for DRNNs with Markovian switching are derived by means of the vector $ {\mathcal {L}}$ -operator differential inequality. When the input is zero, an improved criterion on exponential stability is obtained. Two numerical examples are provided to examine the correctness of the derived results. [ABSTRACT FROM AUTHOR]

The paper is concerned with the problem of input-to-state stability (ISS) for nonlinear delay systems with large delay periods (LDP). The concepts of the length rate of LDP and the frequency of LDP are introduced. First the considered system is converted into a switched delay system which may include an unstable subsystem. Then based on a piecewise Lyapunov functional, the ISS properties of the systems are developed under the constraints of the length rate and the frequency of LDP. ISS for a special kind of nonlinear delay systems is also considered and the conditions of nonlinear matrix inequalities (NLMIs) are proposed to guarantee the ISS properties of such a system. A numerical example and an example of a series DC motor are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization problem is investigated for a class of nonlinear delayed dynamical networks with heterogeneous impulsive effects. The intrinsic properties of heterogeneous impulses are that impulsive strengths are inhomogeneous in both time and space domains, i.e., the impulsive effect in each node is not only nonidentical from each other, but also time-varying at different impulsive instants. The purpose of the addressed problem is to derive synchronization criteria such that, the nonlinear delayed dynamical networks with heterogeneous impulses can be synchronized to a desired state. By means of a time-dependent Lyapunov function and the comparison principle, several sufficient conditions are established under which nonlinear dynamical networks with heterogeneous impulsive effects are exponentially synchronized to a desired state. An example is given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing time-varying quantizers for the stabilization of switched linear systems with quantized output and switching delays. The detection delays of switches are assumed to be time-varying but bounded, and the dwell time of the switching signal is assumed to be larger than the maximum delay. Given a switching controller, we analyze reachable sets of the closed-loop state by using a common Lyapunov function and then construct a quantizer that guarantees asymptotic stability. A sufficient condition for the existence of such a quantizer is characterized by the maximum switching delay and the dwell time. [ABSTRACT FROM AUTHOR]

This paper is concerned with the exponential stability and stabilization of memristive neural networks (MNNs) with delays. First, we present some generalized double-integral inequalities, which include some existing inequalities as their special cases. Second, combining with quadratic convex combination method, these double-integral inequalities are employed to formulate a delay-dependent stability condition for MNNs with delays. Third, a state-dependent switching control law is obtained for MNNs with delays based on the proposed stability conditions. The desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples. [ABSTRACT FROM AUTHOR]

Multiagent systems (MASs) are ubiquitous in our real world. There is an increasing attention focusing on the consensus (or synchronization) problem of MASs over the past decade. Although there are numerous results reported on the convergence of a discrete-time MAS based on the infinite products of matrices, few results are on the convergence rate. Because of the switching topology, the traditional eigenvalue analysis and the Lyapunov function methods are both invalid for the convergence rate analysis of an MAS with a switching topology. Therefore, the estimation of the convergence rate for a discrete-time MAS with time-varying delays remains a difficult problem. To overcome the essential difficulty of switching topology, this paper aims at developing a contractive-set approach to analyze the convergence rate of a discrete-time MAS in the presence of time-varying delays and generalized coupling coefficients. Using the proposed approach, we obtain an upper bound of the convergence rate under the condition of joint connectivity. In particular, the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients, which have been widely applied in the existing works on this topic. As an application of the main results, we will show that the classical Vicsek model with time delays can realize synchronization if the initial topology is connected. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the passivity analysis for switched neural networks subject to stochastic disturbances and time-varying delays. First, using the multiple Lyapunov functions method, a state-dependent switching law is designed to present a stochastic passivity condition. Second, a hysteresis switching law involving both the current state and the previous value of the switching signal are presented to avoid chattering resulted from the state-dependent switching. Third, based on the average dwell-time approach, a class of switching signals is determined to guarantee the switched neural network stochastically passive. Finally, three numerical examples are provided to illustrate the characteristics of three proposed switching laws. [ABSTRACT FROM PUBLISHER]

An energy-efficient fast array multiplier is proposed and designed. The multiplier operates in a left-to-right mode enabling a full overlap between reduction of partial products in carry-save form and the final addition producing the product. The design is based on the left-to-right carry-free (LRCF) multiplier. It differs from the LRCF multiplier in a much smaller on-the-fly conversion circuit of $O(n)$ size and the use of radix-4 full adders in the conversion. The new converter produces the most-significant half of the product during the reduction process. It eliminates the most-significant part of the final adder. The least-significant half of the product is obtained with a carry-ripple adder during the reduction. Thus conversion of the carry-save form of accumulated partial products to the conventional product does not add any delay to the total time of the multiplier. Several right-to-left, left-to-right multipliers and tree multipliers are designed for 16, 24, 32, and 56 bits, and radices 2 and 4, synthesized in 90 nm technology and compared, demonstrating the advantages and disadvantages of the proposed design with respect to area, delay, power, and energy. We considered both truncated and full-precision multipliers. The proposed multiplier has lower delay, area, power, and energy than other considered types of array multipliers. Its advantages grow with the increase in precision. As expected, it is slower than a tree multiplier but it has smaller area, power, and energy. [ABSTRACT FROM PUBLISHER]