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In the article, we establish some monotonicity and convexity (concavity) properties for certain combinations of polynomials and the Ramanujan R-function by use of the monotone form of L’Hôpital’s rule and present serval new asymptotically sharp bounds for the Ramanujan R-function that improve some previously known results.

In this paper, we address the distributed convex optimization problems for multi-agent systems. In our research, it is assumed that each agent in the multi-agent system could merely interact with its neighbors via a directed graph and is available to its own cost function. We then utilize the push-sum distributed dual averaging (PS-DDA) algorithm to tackle with the distributed optimization problem. However, we consider that there exist subgradient delays in PS-DDA algorithm. The proof of the main result which shows that the PS-DDA algorithm with subgradient delays converges and the error possesses sublinear growth of a rate O ( τ 2 T − 0.5 ) , where T denotes the total amount of iterations, is detailed presented in this paper. Finally, a numerical example is simulated to show the performance of the algorithm we study in this paper.

This paper addresses the finite-time state estimation problem for semi-Markovian jump neural networks with sensor nonlinearities under the consideration of leakage delay and time-varying delay. The modes of original system and desired estimator are supposed to be asynchronous. Some sufficient conditions are proposed to guarantee the finite-time boundedness as well as mixed H ∞ and passive performance of the error system in terms of constructing Lyapunov–Krasovskii functionals. By utilizing affine Bessel-Legendre inequalities, a less conservative result can be achieved. By virtue of linear matrices inequalities approach, the asynchronous state estimator gains are obtained. Two numerical examples are provided to demonstrate the less conservativeness and effectiveness of our method.

This paper addresses the problem of synchronization control of neutral-type neural networks with sampled-data, where sampled data will be over a communication network before received by controller. Generally, the communication network is with a bandwidth-limited communication channel. To reduce network burden, an event-triggered scheme is designed between the sampler and communication network. A weak synchronization conditions are derived by using our proposed integral inequality. Finally, a numerical example is given to illustrate the effectiveness and advantage of the proposed results.

In this paper, the problem of fixed-time outer synchronization over double-layered neuron-based networks with uncertain parameters in nonlinear nodes dynamics and delayed coupling among the nodes is studied. To solve the problem, we propose a delay-dependent controller. Via employing Lyapunov stability theory for the double-layered networks, some sufficient criteria for the fixed-time outer synchronization are provided. To guarantee that the uncertain parameters are identified, an adaptive update identification law is designed. The designed controllers and the sufficient criteria can be applied not only to fixed-time synchronization of double-layered directed networks, but also to fixed-time synchronization of double-layered undirected networks. Our results indicate that the fixed settling time is related to the designed controllers, the size for neuron-based networks, the number of uncertain parameters for each neuron and the dimension of each neuron node in the fixed-time synchronization. Simulation examples illustrating the results are included.

This paper addresses the problem of H∞ control for an uncertain discrete-time Markov jump system subject to multiple intermittent sensor faults. The intermittent fault considered in this paper is formulated as a probabilistic event and is additive to the normal signal of a sensor in systems. The occurrence of the intermittent fault is assumed to satisfy the Bernoulli random binary distribution which takes values of either 0 or 1. The nonlinearity is related to time-varying delay and satisfies a sector-bounded condition. The Markov chain is considered as finite piecewise-constant. To keep the desired performance of the faulted system, a dynamic full-order output-feedback controller is presented. By using the Lyapunov method and inequality techniques, exponential mean-square stability criteria of the fault-free closed-loop system are obtained and a design of the dynamic full-order output-feedback controller is given. Finally, a numerical example is given to show effectiveness and advantage of the obtained results.

This paper is concerned with the problem of event triggering H ∞ synchronization control for discrete-time switched complex networks via quasi-time asynchronous controllers. One event triggering mechanism is introduced with the triggering parameters depending on triggering states. Applying quasi-time dependent multiple Lyapunov functions and the mode-dependent average dwell time technique, quasi-time dependent synchronization conditions are obtained with a lower weighted performance index. And then, a quasi-time dependent asynchronous controller is designed with quasi-time dependent control gains in each triggering interval. In addition, not only no more than one switching, but also multiple switchings are taken into account in each triggering interval, by which the assumption in some existing results is relaxed. Finally, the proposed result is applied to the PWM-driven boost converter.

The problem for fixed-time outer synchronization of double-layered multi-weighted coupled complex networks with stochastic effects is considered in this paper. To suppress chattering in synchronization, an adaptive chattering-free control algorithm is designed. Based upon the Lyapunov stability theory, some sufficient criteria for the adaptive stochastic outer synchronization are proposed. The designed adaptive chattering-free controller and the sufficient conditions can be applicable to not only the fixed-time stochastic synchronization of double-layered multi-weighed undirected networks, but also the fixed-time stochastic synchronization of double-layered multi-weighted directed networks. Our theoretical results indicate that the settling time is related to the size of dynamic networks, the dimension of each node and the designed adaptive controllers in the fixed-time stochastic outer synchronization. The effectiveness of our derived theoretical framework is illustrated via simulation examples.

This paper considers the problem of reliable filter design for discrete-time neural networks subject to Markovian jumping parameters and time-varying delay. Firstly, based on a matrix inequality, a new sufficient condition, which guarantees the existence of a reliable filter such that the resulting filtering error system is stochastically stable and extended dissipative, is established. Second, a less conservative stability criterion for neural networks is proposed. Then, the condition for the solvability of the filter design problem is given in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are given to illustrate the effectiveness and advantages of the proposed filter design scheme.

The paper studies the prescribed performance output regulation problem for a class of nonlinear uncertain strict-feedback systems which are driven by nonlinear exosystems. Fuzzy logic systems (FLSs) are used to approximate the unknown functions. A fuzzy adaptive observer is designed to estimate the system state. A fuzzy internal model is designed to reject disturbance. Simultaneously, a parameter-type Lyapunov function and L function are designed to ensure the prescribed performance of the system. As illustrated by example, the proposed prescribed performance fuzzy adaptive output feedback control scheme is shown to guarantee semi-globally uniformly ultimately bounded, and the dynamic performance and steady-state performance of the tracking error are dependent on the prescribed performance functions.

This paper discusses a neural dynamic surface control (DSC) problem for a class of nonlinear systems in the case of full-state constraints and unknown disturbances. Incorporating an improved DSC method and the neural networks (NNs) approximation with the minimization parameter method, an improved neural DSC approach is constructed for the studied system. By introducing a novel barrier Lyapunov function (BLF) in the design steps, the issue of full-state constraints existing in the system can be solved. The highlighting features of the proposed control method are that only one online estimation parameter should be updated, and the same stability property as the conventional backstepping method can be reserved. The transgressions of full state constraints never occur in the case of disturbances. By the Lyapunov stability analysis, all the signals of the closed-loop system are ultimately bounded. Finally, two simulation examples display the effectiveness of the proposed approach.

The saturation input control problem of discrete-time networked systems via adaptive event-triggered communication scheme is discussed in this paper. The criteria are derived by utilising a new Lya...

This paper is concerned with the observer-based control problem for Markovian jump delay systems with parameter uncertainties using quantized measurements. The parameter uncertainties are assumed to be norm bounded. The aim is to design a suitable observer-based controller which guarantees the stochastic stability of the resulting closed-loop system with a prescribed mixed passivity and H ∞ performance index. A novel stability criterion is obtained by constructing a mode-dependent Lyapunov–Krasovskii functional based on the delay-partitioning technique. Then, with the novel stability criterion, sufficient conditions for the solvability of the presented observer-based controller design problem are derived. All the results obtained in this paper can be tackled by a feasibility problem in terms of linear matrix inequalities. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed methods.

This paper considers the finite time state estimation problem of complex-valued bidirectional associative memory (BAM) neutral-type neural networks with time-varying delays. By resorting to the Lyapunov function approach, the Wirtinger inequality and the reciprocally convex approach, a delay-dependent criterion in terms of LMIs is established to guarantee the finite-time boundedness of the error-state system for the addressed system. Meanwhile, an effective state estimator is designed to estimate the network states through the available output measurements. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results.