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This paper investigates the stability problem for discrete-time genetic regulatory networks (GRNs) with time-varying delays. A new stability criterion is established by utilizing the discrete Wirtinger-based inequality and a new constraint condition on feedback regulatory function which are used for the first time in the stability analysis of GRNs. Two numerical examples are provided to demonstrate...
We propose a boundary state feedback control law for a one-dimensional connected string equation with general external disturbance entering the control end. Sliding mode control is adopted for investigation. There are two steps: A sliding surface is first found so that the system on the sliding surface is exponentially stable; and then a variable structure feedback control is designed to satisfy the...
This paper studies the well-posedness, stochastic stability and performance of the spatially interconnected discrete-time Markovian jump time-delay systems. By using the strict linear matrix inequalities (LMIs), a sufficient condition is obtained to guarantee the desired properties, which gives a theoretical foundation for the further research. In addition, the transition of the jumping parameters...
The finite-time H∞ control problem for a class of nonlinear continuous-time descriptor semi-Markov jump systems is discussed in this paper. Firstly, sufficient conditions on singular stochastic finite-time boundness for nonlinear continuous-time descriptor semi-Markov jump systems are established, then the results are extended to singular stochastic H∞ finite-time boundness for such systems. Secondly,...
This paper is concerned with the problem of asymptotical stability for neutral system. The delay variation is divided into two unequal subintervals and some Lyapunov-Krasovskii functionals are defined on the obtained subintervals. The reciprocally convex technique is used to deal with the derivative of the Lyapunov-Krasovskii functionals. Two improved delay-dependent criteria are derived in terms...
This paper is concerned with the stability and stabilization analysis for another usual class of Markov jump linear systems(MJLSs). In this paper, some of the system's regimes are difficult or unable to classify accurately, and this problem can be solved via recombined the probability space of the system. As a result, the necessary and sufficient conditions for stochastic stability of the system are...
This paper deals with stochastic finite-time stabilization of a discrete-time positive Markov jump linear system with time-delay. Firstly, the stochastic finite-time stability of the positive Markov jump linear system with time-delay is proved to be equivalent to the finite-time stability of a deterministic positive linear system with time-delay, as well as the finite-time stability of a deterministic...
This paper investigates the problem of stability analysis of neural networks with time-varying delay. Some augmented double integral term and triple integral terms are introduced to the Lyapunov-Krasovskii functional (LKF). And the derivative of the LKF is estimated by the free-matrix-based integral inequality. Then, a less conservative stability criterion is derived. Finally, a numerical example...
This paper investigates the stability and stabilization for switched systems with all modes unstable. Firstly, a class of periodic switching signal is proposed to ensure that the considered system is global asymptotical stability (GAS) on continuous-time interval. The quadratic Lyapunov function is permitted to increase on the part of a complete switching period. Secondly, the state feedback controllers...
This paper focuses on the admissibility analysis of singular fractional order systems. A novel stability criterion of normal fractional order systems is introduced first. An essential remark is provided on the distribution of eigenvalue of system matrix. Then a necessary and sufficient condition for the admissibility of singular fractional order systems is derived. All the results are obtained in...
This paper investigates the stabilizability of linear impulsive systems. The fact that some linear impulsive systems may be asymptotically stabilizable even though they are not stable under any consistent impulsive law is indicated by a numerical example. A sufficient condition for the asymptotical stabilizability of linear impulsive systems is presented and then the state-dependent impulsive law...
In this paper, a derivative Lorenz chaotic system is considered and the stability of equilibrium points and the existence of Hopf bifurcation are investigated by center manifold theorem and normal form theory. Besides, we designed a washout controller such that the derivative Lorenz chaotic system undergoes a controllable Hopf bifurcation. By the calculation of the first Lyapunov coefficient and adjust...
The stabilization of Itô stochastic time-varying systems is studied via receding horizon control (RHC) in this paper. By using stochastic maximum principle we obtain the explicit solution of the receding horizon control. Based on monotonically non-increasing of optimal cost and stochastic Lyapunov stability theory, a necessary and sufficient stabilization condition on the terminal weighting matrix...
In this paper, the problem of delay-dependent stability criterion for Takagi-Sugeno systems with time-varying delay is investigated. Firstly, a novel augmented Lyapunov-Krasovskii functional is chosen. Then, a less conservative stability criterion is obtained via a newly developed free-matrix-based integral inequality. Finally, two numerical examples on time-delay stability analysis are given to demonstrate...
This paper is concerned with the stability analysis for impulsive stochastic high-order Hopfield-type neural network with time-varying delay. Utilizing the Lyapunov-Krasovskii Functional, some new conditions for ensuring asymptotically stability of the neural network are devised. Numerical examples show that the results are effectiveness.
This study aims at investigating the issues of stability and stabilization for time delay quadratic discrete-time systems. First of all, provided a locally asymptotically stable zero equilibrium point of the quadratic system and some other polytope in the state space containing the origin, a delay-independent sufficient condition judging whether this polytope belongs to the domain of attraction (DA)...
This paper investigates the problem of the delay-dependent stability of neutral systems with mixed-delay and time-varying structured uncertainties. Different from the existing techniques, some less conservative criteria are presented by combining the free-weighting matrix technique and Wirtinger-based integral inequality technique. Numerical examples illustrate the improvement of this approach over...
In this paper, the stabilization bound problem for time-delay singularly perturbed systems (SPSs) with actuator saturation is considered. Based on the Lyapunov-Kravoskii functional and linear matrix inequality (LMI) approach, the design method of stabilization controller for SPSs with time-delay and actuator saturation is proposed. Then, the problem of estimating the domain of attraction depending...
According to the idea of “extended state”, a new control strategy is presented to stabilize Timoshenko beam with boundary disturbances. Similar to the active disturbance rejection control (ADRC) approach, first, the disturbance is estimated by a high gain observer, and then attenuated via the feedback channel. It is shown that the closed-loop system is exponentially stable by Lyapunov method, if the...
This paper aims to investigate the exponential stability of general stochastic functional differential systems with delayed impulses. By using the average impulsive interval and the Lyapunov function method, we derive some sufficient conditions for exponential stability, which are less conservative than those existing results based on the supremum or infimum of impulsive interval and more convenient...
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