An Adaptive Model of Demand Adjustment in Weighted Majority Games

This paper presents a simple adaptive model of demand adjustment in cooperative games and analyzes this model in weighted majority games. In the model, a randomly chosen player sets her demand to the highest possible value subject to the demands of other coalition members being satisfied. This basic process converges to the aspiration set. By introducing some perturbations into the process, we show that the set of separating aspirations, i.e., demand vectors in which no player is indispensable in order for other players to achieve their demands, is the one most resistant to mutations. We then apply the process to weighted majority games. We show that in symmetric majority games and in apex games, the unique separating aspiration is the unique stochastically stable one.

Mixed H∞ and Passivity Performance Analysis of Interfered Digital Filters with Markovian Jumping Parameters and Delays

This paper deals with the problem of mixed [Formula: see text] and passivity performance analysis of digital filters subject to Markovian jumping parameters, external disturbances, time delays and bounds of the nonlinearity functions. By employing Lyapunov theory and matrix decomposition technique, a novel sufficient condition is established. The proposed criterion ensures that the underlying system is stochastically stable and satisfies a mixed [Formula: see text] and passivity performance index simultaneously. The obtained criterion can also be employed to solve the [Formula: see text] problem or the passivity problem in a unified framework. Moreover, the problem is formulated to obtain optimal mixed [Formula: see text] and passivity performance index of the interfered digital filters. The effectiveness and superiority of our proposed results are illustrated by three examples.

Delay-dependent passivity analysis of nondeterministic genetic regulatory networks with leakage and distributed delays against impulsive perturbations

This work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distributed delays. The main aim of this paper is constructing a passivity-based criteria under impulsive perturbations such that the proposed GRNs are stochastically stable. Based on the Lyapunov functional method and Jensen’s integral inequality, we obtain a new set of novel passivity based delay-dependent sufficient condition in the form of LMIs, which can be determined via existing numerical software. Finally, we propose numerical simulations to show the efficiency of the proposed method.

Robust Fast Adaptive Fault Estimation for T-S Fuzzy Markovian Jumping Systems with Mode-Dependent Time-Varying State Delays

This paper studies the problem of actuator fault estimation for a class of T-S fuzzy Markovian jumping systems, which is subject to mode-dependent interval time-varying delays and norm-bounded external disturbance. Based on the given fast adaptive estimation algorithm and by employing a novel Lyapunov–Krasovskii function candidate, a robust fault estimation scheme is proposed to estimate faults whose derivative is bounded. With this improved method, the proposed fault estimator minimizes the effect of disturbance on the estimation error and reduces the conservatism of systems stability results simultaneously. To be specific, an improved mode-dependent criterion for the existence of the fault estimation observer is established to guarantee the error dynamic system to be stochastically stable with a prescribed H ∞ performance and reduce the conservatism of designing procedure. Finally, three numerical examples are given to show the effectiveness of the proposed method.

Fuzzy-Model-Based Control for Markov Switching Singularly Perturbed Systems with the Stochastic Communication Protocol

This work is concerned with the H ∞ control for Markov switching singularly perturbed systems with the stochastic communication protocol. To coordinate the data transmission and save the bandwidth usage, the stochastic communication protocol with a compensator is applied to schedule the information exchange. The goal of this work is to design a joint-Markov-process-based controller such that the resulting system is stochastically stable with prescribed performance. Based on the Lyapunov functional technique, a sufficient condition is derived to ensure the existence of the achieved controller. Finally, the effectiveness and correctness of the developed results are verified by the simulation example.

Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response

In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results.

Event-Triggered Dissipative Filter Design for Semi-Markovian Jump Systems with Time-Varying Delays

This paper deals with the event-triggered dissipative filtering problem for semi-Markovian jump systems with time-varying delays. The purpose is to design a filter which guarantees that the filtering error system is not only stochastically stable but also satisfies dissipativity. First, based on Lyapunov–Krasovskii theory and matrix integral inequality, a sufficient condition is established for the existence of such a filter. Then, the codesign method of event-triggered matrices and the desired filter parameters is proposed. Finally, two numerical examples are given to illustrate the advantages and validity of the scheme developed in this paper.

Robust H∞ filtering for Markovian jumping static neural networks with time-varying delays

The problem of robust H∞ filtering for Markovian jumping static neural networks with time-varying delays is considered in this paper. The effect of the activation function on the time delays is comprehensively considered. Based on Wirtinger inequality, a new inequality is quoted to solve the Lyapunov functions with the double-integral terms. Then, a less conservative result on the robust H∞ filtering is obtained, which guarantees the resulting error systems stochastically stable and satisfies a prescribed H∞ performance index. The effectiveness of the developed results is finally demonstrated by numerical examples.