Shouming Zhong

Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems

This paper develops a fractional-order sliding mode based extremum seeking controller (FO SM-ESC) for the optimization of nonlinear systems. The proposed FO SM-ESC, involving an FO derivative function 0 D t q sgn ( e ) , 0 ? q < 1 is shown to achieve faster tracking and higher control accuracy than the integer-order (IO) SM-ESC. The tradeoff between control performance and parameters selection is analyzed and visualized. The comparison between the FO/IO SM-ESC is given to reveal the potential advantages of the FO controller over the IO controller. Simulation and experimental results show that the FO SM-ESC can have a faster convergence speed and a smaller neighborhood around the optimal operational point.

Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals☆

This paper is concerned with the problem of finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. In order to reduce conservatism, a new Lyapunov-Krasovskii functional is constructed. Based on the derived condition, the reliable H∞ control problem is solved, and the system trajectory stays within a prescribed bound during a specified time interval. Finally, numerical examples are given to demonstrate the proposed approach is more effective than some existing ones.

Improved delay-dependent stability criterion for neural networks with time-varying delay

In this paper, the problem of delay-dependent asymptotic stability criterion for neural networks with time-varying delay has been considered. A new class of Lyapunov functional which contains a triple-integral term is constructed to derive some new delay-dependent stability criteria. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Delay-dependent robust stability and control synthesis for uncertain switched neutral systems with mixed delays

This article discusses the delay-dependent robust stability of a class of uncertain switched neutral system with mixed delay and time-varying structure. Firstly, delay-dependent stability of switched neutral system without uncertainty has been obtained, and further robust stability of the uncertain system has reached. Next, state-feedback controls have been derived for the switched neutral system, whose subsystems are not necessarily stable. Three numerical examples are given to illustrate the proposed methods.

Robust stability analysis for discrete-time stochastic neural networks systems with time-varying delays

In this paper, the mean square exponential stability is investigated for a class of discrete-time stochastic neural networks with time-varying delays and norm-bounded uncertainties. Based on Lyapunov stability theory and stochastic approaches, delay-dependent criteria are derived to ensure the robust exponential stability in the mean square for the addressed system. Meantime, by using the numerically efficient Matlab LMI Toolbox, a example is presented to show the usefulness of the derived LMI-based stability condition.

Finite-time boundedness of state estimation for neural networks with time-varying delays

In this paper, we study the finite-time boundedness problem for neural networks with time-varying delays. By introducing a newly augmented Lyapunov-Krasovskii functional and considering the relationship between time-varying delays and their upper delay bounds, sufficient condition of state estimation for neural networks with time-varying delays is presented and proved by using convex polyhedron method and novel activation function conditions. Finally, a numerical example is given to illustrate the efficiency and less conservative character of the proposed method.

Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays

This paper studies impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays and Neumann boundary conditions. By employing the topological degree theory, delay differential inequality with impulses, linear matrix inequality (LMI) and Poincare inequality, a set of sufficient conditions are derived to ensure the existence, uniqueness and global exponential stability of the equilibrium point. These global exponential stability conditions depend on the reaction-diffusion term. A comparison between our results and the previous results shows that our results establish a new set of stability criteria for reaction-diffusion neural networks and have improved the previous results.

Improved delay-dependent stability criteria for neural networks with two additive time-varying delay components

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method. Keywords—Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.

Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates

Abstract In this paper, the problem of stochastic stability criterion of Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates is considered. Some new delay-dependent stability criteria are derived by choosing a new class of Lyapunov functional. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Novel delay-dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations

This paper investigated the problem of delay-dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations. A piecewise delay method is used in this paper, the variation interval of the time delay is divided into two subintervals by introducing its central point. Then, by employing the new Lyapunov-Krasovskii functional and linear matrix inequality technique, some new sufficient conditions are obtained. At last, numerical examples are provided to demonstrate the effectiveness of the obtained results.