On delay-dependent robust stability of neutral systems

The delay-dependent robust stability of uncertain linear neutral systems with delays is investigated. Both discrete-delay-dependent/neutral-delay-independent and neutral-/discrete- delay-dependent stability criteria will be developed. The proposed stability criteria are formulated in the form of linear matrix inequalities and it is easy to check the robust stability of the considered systems. By introducing certain Lyapunov-Krasovskii functional the mathematical development of our result avoids model transformation and bounding for cross terms, which lead to conservatism. Finally, numerical example is given to indicate the improvement over some existing results.     

Delay-dependent stability and stabilization criteria of networked control systems with multiple time-delays

This paper deals with the problem of delay-dependent stability and stabilization for networked control systems（NCSs）with multiple time-delays. In view of multi-input and multi-output（MIMO） NCSs with many independent sensors and actuators, a continuous time model with distributed time-delays is proposed. Utilizing the Lyapunov stability theory combined with linear matrix inequalities（LMIs） techniques, some new delay-dependent stability criteria for NCSs in terms of generalized Lyapunov matrix equation and LMIs are derived. Stabilizing controller via state feedback is formulated by solving a set of LMIs. Compared with the reported methods, the proposed methods give a less conservative delay bound and more general results. Numerical example and simulation show that the methods are less conservative and more effective.     

基于切换模糊模型和分段Lyapunov函数的T-S模糊系统时滞依赖H∞控制

研究了离散时滞T-S模糊系统的H无穷控制问题. 首先, T-S模糊系统被转换成等价的切换模糊系统, 基于分段Lyapunov函数, 给出了该系统带有H无穷性能的时滞依赖稳定化控制方法. 所得结论可以用一组线性矩阵不等式表示. 由于考虑了子系统间的相互关系, 因此所得结论较以往结果具有更小的保守性. 最后, 仿真例子说明了所提方法的有效性.     

New delay-dependent non-fragile H∞ observer-based control for continuous time-delay systems

The problem of the delay-dependent non-fragile H_∞ observer-based control for a class of continuous time-delay systems is investigated in this paper. The additive gain variations under consideration are contained in both the controller gain and obhsiunserver gain. Delay-dependent criteria are derived to guarantee the stability of the non-fragile H_∞ observer-based control system using the Lyapunov functional approach. The controller and observer gains are given from the LMI feasible solutions. Based on the result of this paper, the constraint of matrix equality is not necessary for designing the non-fragile H_∞ observer-based controls. Computer software Matlab can be applied to solve all the proposed results. Finally, a numerical example is illustrated to show the improvement of this paper.     

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.     

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.     

l2-l∞ filter design for discrete-time singular Markovian jump systems with time-varying delays

The problem of l₂-l_∞ filter design for discrete-time singular systems with Markovian jump and time-varying delays is investigated in this paper. By using the delay partitioning technique, a delay-dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l₂-l_∞ performance index. Based on the derived condition, the full-order and reduced-order filters with mode-independent characterization are designed in a unified framework. The corresponding filter parameters can be obtained by solving a set of linear matrix inequalities. The reported results not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Two numerical examples are provided to illustrate the effectiveness of the proposed methods.     

Improved delay-dependent stability analysis for neural networks with time-varying delays

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with time-varying delays is considered. A new class of Lyapunov functional is proposed by considering the information of neuron activation functions adequately. By using the delay-partitioning method and the reciprocally convex technique, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the derived method.