Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays

This paper concerns the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainties. A new method based on linear matrix inequalities is presented that makes it easy to calculate both the upper stability bounds on the delays and the free weighting matrices. Since the criteria take the sizes of the neutral- and discrete-delays into account, it is less conservative than previous methods. Numerical examples illustrate both the improvement this approach provides over previous methods and the reciprocal influences between the neutral- and discrete-delays.     

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality (LMI) approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closedloop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.     

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality （LMI） approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed- loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.     

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.     

Robust delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays

This paper is concerned with the robust delay-dependent exponential stability of uncertain stochastic neural networks (SNNs) with mixed delays. Based on a novel Lyapunov-Krasovskii functional method, some new delay-dependent stability conditions are presented in terms of linear matrix inequalities, which guarantee the uncertain stochastic neural networks with mixed delays to be robustly exponentially stable. Numerical examples are given to illustrate the effectiveness of our results.     

Robust delayed-state-feedback stabilization of uncertain stochastic systems

Due to time spent in computation and transfer, control input is usually subject to delays. Problems of deterministic systems with input delay have received considerable attention. However, relatively few works are concerned with problems of stochastic system with input delay. This paper studies delayed-feedback stabilization of uncertain stochastic systems. Based on a new delay-dependent stability criterion established in this paper, a robust delayed-state-feedback controller that exponentially stabilizes the uncertain stochastic systems is proposed. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.     

Delay-dependent robust stability for neutral systems with mixed discrete-and-neutral delays

This paper focuses on the problem of delay-dependent robust stability of neutral systems with different discrete-and neutral delays and time-varying structured uncertainties. Some new criteria are presented, in which some flee weighting matrices are used to express the relatiomhips between the terms in the Leibniz-Newton formula. The criteria include the information on the size of both neutral-and-discrete delays. It is shown that the present results also include the results for identical discrete-and-neutral delays as special cases.A numerical example illustrates the improvement of the proposed methods over the previous methods and the influences between the discrete and neutral delays.     

Delay-dependent robust stability for neutral systems with mix discrete-and-neutral delays

This paper focuses on the problem of delay-dependent robust stability of neutral systems with different discrete-and-neutral delays and time-varying structured uncertainties. Some new criteria are presented, in which some free weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. The criteria include the information on the size of both neutral-and-discrete delays. It is shown that the present results also include the results for identical discrete-and-neutral delays as special cases. A numerical example illustrates the improvement of the proposed methods over the previous methods and the influences between the discrete and neutral delays.     

Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.     

Delay-dependent robust stability analysis of uncertain stochastic neural networks with discrete interval and distributed time-varying delays

This paper is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some numerical examples and comparisons are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing results in the literature. Furthermore, the supplementary requirement that the time derivative of discrete time-varying delays must be smaller than the value one is not necessary to derive the results in this paper.     

多面体不确定系统时滞依赖鲁棒预测控制

将线性状态变换引入连续时间多面体不确定时滞系统中,利用线性矩阵不等式(LMI)方法,设计时滞相关型鲁棒预测控制器;通过适当选择Lyapunov函数,推导出闭环系统渐近稳定的充分条件,并且该条件是时滞相关的.仿真算例验证了该方法的有效性.     

Delay-dependent robust stability of uncertain networked control systems with multiple state time-delays

In this paper, delay-dependent robust stability for a class of uncertain networked control systems （NCSs） with multiple state time-delays is investigated. Modeling of multi-input and multi-output （MIMO） NCSs with networkinduced delays and uncertainties through new methods are proposed. Some new stability criteria in terms of LMIs are derived by using Lyapunov stability theory combined with linear matrix inequalities （LMIs） techniques. We analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound （MADB） for the NCSs with the proposed methods. Compared with the reported results, the proposed results obtain a much less conservative MADB which are more general. Numerical example and simulation is used to illustrate the effectiveness of the proposed methods.     

Delay-dependent stabilization of singular Markovian jump systems with state delay

This paper deals with the delay-dependent stabilization problem for singular systems with Markovian jump parameters and time delays. A delay-dependent condition is established for the considered system to be regular, impulse free and stochastically stable. Based on the condition, a design algorithm of the desired state feedback controller which guarantees the resultant closed-loop system to be regular, impulse free and stochastically stable is proposed in terms of a set of strict linear matrix inequalities （LMIs）. Numerical examples show the effectiveness of the proposed methods.     

Global exponential stability analysis for neutral delay-differential systems: an LMI approach

For neutral differential systems with time-varying or constant delays, the problems of determining the global exponential stability and estimating the exponential convergence rate are investigated in this paper. By using the Lyapunov method, some useful criteria of global exponential stability for the systems are derived. These stability conditions are formulated as linear matrix inequalities (LMIs) which can easily be solved by various convex optimization algorithms. Numerical examples are given to illustrate the application of the proposed method.     

Delay-dependent stabilization of linear systems with time-varying state and input delays

The integral-inequality method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: . In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither (A,B₁) nor (A+A₁,B₁) is stabilizable.