Xia Huang

Chaos and hyperchaos in fractional-order cellular neural networks

In this paper, a fractional-order four-cell cellular neural network is proposed and the complex dynamical behaviors of such a network are investigated by means of numerical simulations. Several varieties of interesting dynamical behaviors, such as periodic, chaotic and hyperchaotic motions, are displayed. In addition, it can be found that the network does exhibit hyperchaotic phenomena over a wide range of values of some specified parameter. The existence of chaotic and hyperchaotic attractors is verified with the related Lyapunov exponent spectrum, bifurcation diagram and phase portraits. Meanwhile, the Lyapunov exponents and Poincare sections are calculated for some typical parameters, respectively.

Control of an uncertain fractional order economic system via adaptive sliding mode

This paper addresses the design of sliding mode controller (SMC) for an uncertain chaotic fractional order economic system. A new fraction-integer integral switching surface is constructed to facilitate stability analysis of the closed-loop system. A sliding mode controller is developed to guarantee that sliding mode motion exists on every point of the switching surface and any state outside the surface is driven to reach the surface in a finite time. Moreover, an adaptive SMC is designed in the case that the upper bound of the uncertainties is unknown. Numerical simulations are performed to verify the feasibility and effectiveness of the proposed controllers.

Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay

In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory ...

Fuzzy dissipative control for nonlinear Markovian jump systems via retarded feedback

Abstract This paper deals with the problem of the dissipative control for a class of nonlinear Markovian jump systems through Takagi–Sugeno fuzzy model approach. The transition rates of Markovian process under consideration are assumed to be partly known. We aim to design retarded feedback controllers such that the resulting closed-loop system is stochastically stable and strictly ( Q , S , R ) - θ - dissipative . By introducing a novel augmented Lyapunov functional and some free Markovian switching matrices, some sufficient conditions for the solvability of the above problem are given in terms of linear matrix inequalities. Finally, two numerical examples are given to demonstrate the effectiveness of our proposed approach.

Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback

Abstract This paper focuses on the analysis and design of dissipativity-based fault-tolerant controller for discrete-time nonlinear Markov jump singularly perturbed systems (MJSPSs) which are based on Takagi–Sugeno fuzzy model. A novel strategy is proposed to improve the upper bound of singular perturbation parameter (SPP) ϵ, and the fault-tolerant design is also introduced, namely the susceptible property of systems is made full consideration, to ensure the specified performance of a system. The aim is to design an optimized slow state feedback controller such that the stability of MJSPSs is guaranteed even in faulty case, and the upper bound of the SPP ϵ is improved simultaneously. Utilizing Lyapunov functional technique, a sufficient condition for the existence of controller is shown. Last but not least, the control issue of a series DC motor model as an illustrated example is given to explain the availability of the presented design scheme.

Consensus of third-order nonlinear multi-agent systems

This paper considers the consensus problem of third-order nonlinear multi-agent systems with a fixed communication topology. A consensus protocol is proposed for solving such a problem. By a transformation, the consensus problem is converted to a stability problem, then sufficient consensus criteria are obtained by proposing a novel Lyapunov function. It is shown that consensus can be achieved for a sufficiently large feedback gain, provided that certain quadratic inequalities with respect to two parameters are satisfied. Finally, the effectiveness of the theoretical results is demonstrated through an example.

Global exponential stability for switched memristive neural networks with time-varying delays

This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples.

Design of fuzzy state feedback controller for robust stabilization of uncertain fractional-order chaotic systems

Abstract In this paper, the stabilization problem of uncertain fractional-order chaotic systems is investigated in the case where the fractional order α satisfies 0 α 1 and 1 ≤ α 2 . Firstly, the uncertain fractional-order chaotic system is described by the so-called fractional-order T–S fuzzy model, and then the fuzzy state feedback controller is correspondingly designed. Secondly, sufficient conditions are derived for the robust asymptotical stability of the closed-loop control systems in those two cases. These criteria are expressed in terms of linear matrix inequalities (LMIs), and the feedback gain matrices can be formulated into the solvability of the relevant LMIs. The proposed controller overcomes some defects in traditional control techniques and is easy to implement. Finally, two numerical examples are presented to demonstrate the effectiveness and the feasibility of the robust stabilizing controller and the robust asymptotical stability criteria.

Complex nonlinear dynamics in fractional and integer order memristor-based systems

Abstract In this paper, a fractional-order (and an integer-order) memristor-based system with the flux-controlled memristor characterized by smooth quadratic nonlinearity is proposed and detailed dynamical analysis is carried out by means of theoretical and numerical methods. To be more specific, stability of each equilibrium point in the equilibrium set is analyzed for the integer-order memristive system. Meanwhile, dynamical behavior depending on the initial states of the memristor is investigated and dynamical bifurcation depending on the slope of the memductance function is also considered. The bifurcation analysis is verified by numerical methods, including phase portraits, bifurcation diagrams, Lyapunov exponents spectrum, and Poincare mappings. For the fractional-order case, based on the fractional-order stability theory, stability analysis is carried out just for a certain equilibrium point. Moreover, bifurcation behavior depending on the incommensurate order is discussed by virtue of numerical methods based on the Adams–Bashforth–Moulton algorithm. This paper indicates how the fractional order model and the initial state of the memristor extend the dynamical behaviors of the traditional chaotic systems.

Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays

This work investigates the dissipativity and stability analysis problems for Markov jump generalized neural networks subject to time-varying interval delays. The aim of the present study is to determine whether the new dissipativity and stability criteria with less conservatism could be established for Markov jump generalized delayed neural networks or not. In this connection, a more general dissipative property index inequality is firstly introduced. On basis of fully considering mode-dependent matrices in the Lyapunov–Krasovskii functional, some advantageous negative terms ignored in some existing works are taken into account. By employing some novel integral inequalities and stochastic analysis theory, some available less conservative criteria are developed. Three compared examples are finally shown to explain the reduced conservatism and superiority of the presented criteria for Markov jump generalized delayed neural networks.