On robust stability of time-delay systems with norm-boundeduncertainty

This paper considers the robust stability problem for a class of time-delay systems with norm-bounded, and possibly time-varying uncertainty. Based on the discretized Lyapunov functional approach, a stability criterion is derived. The time-delay is assumed constant and known. Numerical examples show that the results obtained by this new criterion significantly improve the estimate of the stability limit over some existing results in the literature     

平衡倒立摆系统的鲁棒稳定性分析

本文介绍了一种非线性系统的频域稳定性判据,这种方法把非线性系统的稳定性总理２转化为级数的收敛问题,文中重点利用该稳定性判据,讨论了倒立摆系统的稳定性问题,所得的理论分析结果与实验数据基本吻合。     

An extended frequency-domain stability criterion for a class of sampled-data systems

A new frequency-domain stability criterion employing a Popov-type multiplier is obtained for a class of nonlinear sampled-data control systems containing a monotonically nondecreasing nonlinearity. This criterion is an extension of previous results, in that unlike other criteria of this type, no upper bound is placed on the derivative of the nonlinearity. An example is given in which this new criterion is used to obtain stability conditions for a non-linear sampled-data system. These conditions are less restrictive than those obtained using other stability criteria.     

An improved stability test and stabilisation of linear time-varying systems governed by second-order vector differential equations

In this article, the problems of exponential stability analysis and stabilisation of linear time-varying systems described by a class of second-order vector differential equations are considered. Using bounding techniques on the trajectories of a linear time-varying system, the stability problem of the time-varying system is transformed to that of a time-invariant system and a new sufficient condition for the exponential stability is obtained. Moreover, the new criterion is proven to be superior to a test presented in the recent literature. Finally, the proposed criterion is applied to the exponential stabilisation problem via state feedback. The results are illustrated by several numerical examples.     

中立型变时滞系统的鲁棒稳定性

考虑不确定中立型变时滞系统的鲁棒稳定性问题. 首先, 引入新的变量来代替系统的不确定性; 然后, 通过构造一般形式的Lyapunov-Krasovskii泛函、使用积分不等式并引入自由矩阵, 得到了基于线性矩阵不等式的系统稳定性判据. 该结论与中立型时滞, 离散时滞及其导数均相关, 具有较小的保守性. 最后, 通过仿真算例说明了所得到的结论在保守性上优于现存的结果以及中立型时滞, 离散时滞及其导数三者之间的关系.     

Stability analysis and stabilization of Markovian jump systems with time‐varying delay and uncertain transition information

The paper investigates the problems of stability and stabilization of Markovian jump systems with time‐varying delays and uncertain transition rates matrix. First, the stochastic scaled small‐gain theorem is introduced to analyze the stability of the Markovian jump system. Then, a new stability criterion is proposed by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. The proposed stability condition is demonstrated to be less conservative than other existing results. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a new precise triangle inequality and a new Lyapunov‐Krasovskii functional. Moreover, a controller design criterion is presented according to the stability criterion. Furthermore, the transition rate matrix is treated as partially known and with uncertainty, and the relevant stability and stabilization criteria are proposed. Finally, 3 numerical examples are provided to illustrate the superior result of the stability criteria and the effectiveness of the proposed controller design method.     

Delay-dependent Stability of Recurrent Neural Networks with Time-varying Delay

This paper investigates the delay-dependent stability problem of recurrent neural networks with time-varying delay. A new and less conservative stability criterion is derived through constructing a new augmented Lyapunov-Krasovskii functional (LKF) and employing the linear matrix inequality method. A new augmented LKF that considers more information of the slope of neuron activation functions is developed for further reducing the conservatism of stability results. To deal with the derivative of the LKF, several commonly used techniques, including the integral inequality, reciprocally convex combination, and free-weighting matrix method, are applied. Moreover, it is found that the obtained stability criterion has a lower computational burden than some recent existing ones. Finally, two numerical examples are considered to demonstrate the effectiveness of the presented stability results.     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.     

Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling

This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria.     

A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices

This paper deals with the problem of robust stability for a class of uncertain linear neutral systems. The uncertainties under consideration are of norm-bounded type and appear in all system matrices. A new delay-dependent stability criterion is obtained and formulated in the form of linear matrix inequalities (LMIs). Neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criterion. Numerical examples show that the results obtained in this paper significantly improve the estimate of the stability limit over some existing results in the literature.