Stability Analysis for Time-delay Systems with Nonlinear Disturbances via New Generalized Integral Inequalities

This paper represents a novel less conservative stability criterion for time-delay systems with nonlinear disturbances. The main purpose is to obtain larger upper bound of the time-varying delay. A suitable Lyapunov- Krasovskii functional (LKF) with triple integral terms is constructed. Then, two new generalized double integral (GDI) inequalities are proposed which encompass Wirtinger-based double inequality as a special case. A simple case of the proposed GDI inequality is utilized to estimate double integral terms in the time derivative of the constructed LKF. Further, an improved delay-dependent stability criterion is derived in the form of linear matrix inequalities (LMIs). Finally, some numerical examples are given to illustrate the improvement of the proposed criteria.     

时滞系统时滞相关型稳定性准则

针对常数时滞线性系统的稳定性问题,基于一个适当形式的Lyapunov-Krasovskii泛函,通过利用一个积分不等式,采用时滞分解方法,以线性矩阵不等式的形式给出了时滞系统的时滞相关型稳定性准则.与现有的时滞相关型稳定性结果相比较,所得到的结果具有保守性更好,结构更加简单,且不合有任何多余的矩阵变量等特点,并从理论上进行了严格的证明,解决了现有的稳定性结果绝大多数只是从数值例子说明其有效性的问题.示例说明了所得结果的有效性.     

时滞网络控制系统的模糊控制及稳定性分析

针对网络控制系统(Networked Control Systems,NCSs)中存在的时延问题,给出一种新的网络控制系统的建模方法--离散模糊T-S模型,利用此模型去逼近非线性网络控制系统,并在此模型的基础上应用平行分布补偿原理(Parallel Distributed Compensation,PDC)设计控制器....     

Stability Analysis of Dynamic Systems in the Polynomial Vector-Matrix Representation

This paper suggests frequency-domain stability criteria for homogeneous multiconnected automatic control systems that allow an easy stability analysis of high-order systems of a large dimension. The results are confirmed by mathematical modeling.     

T-S模糊系统的二次稳定

应用LMI(线性矩阵不等式)方法,研究了T-S模糊系统二次稳定性及控制器设计问题.首先,通过考虑模糊系统隶属函数的性质,将原系统进行变换,给出了T-S模糊系统二次稳定的新条件,并提出了基于LMI的控制器设计方法.与现有结果相比,该方法不仅考虑了各子系统间的关系,还考虑到隶属函数的性质,计算量和保守性较小.仿真算例验证了其有效性.     

二次规划问题的新型时滞投影神经网络的稳定性分析

本文针对求解有等式约束的二次规划问题的时滞投影神经网络,提出一种所有神经元皆存在时滞情况的新型网络模型。利用Gronwall不等式和Halanay不等式,严格证明了所提网络模型的全局指数稳定性。研究结果表明,所提网络模型的解能够渐进收敛于原问题的最优解,具有计算迅速和精度较高等特点。数值仿真结果验证了所提网络模型的可行性与有效性。     

Improved Stability Criteria for Discrete-time Delay Systems via Novel Summation Inequalities

This paper is concerned with the stability analysis of linear discrete time-delay systems. New discrete inequalities for single summation and double summation are presented to estimate summation terms in the forward difference of Lyapunov-Krasovskii functional (LKF), which are more general than some commonly used summation inequalities. Through the construction of an augmented LKF, improved delay-dependent stability criteria for discrete time-delay systems are established. Based on this, a time-delayed controller is derived for linear discrete time-delay systems. Finally, the advantages of the proposed criteria are revealed from the solutions of the numerical examples.     

LMI Condition of Quadratic D-stability for a Class of Uncertain Linear Systems

A necessary and sufficient condition of the quadratic D-stability for a class of uncertain linear systems is presented in terms of linear matrix inequality (LMI) technology.Finally,the validity and less conservatism of the obtained results in this paper are illustrated by a benchmark example.     

一类奇异摄动时滞不确定系统鲁棒稳定性

为了解决复杂工业过程控制系统由于工程设计时模型描述的不完全性造成的不稳定,针对一类常见的奇异摄动时滞不确定线性系统,研究了其鲁棒稳定性问题。通过对系统各参数日。范数有界摄动分析,获得了系统时滞有关稳定的充分条件。给出了保证系统稳定的时滞τ及奇异摄动参数ε的上界,在工程设计中为复杂工业过程控制系统稳定边界的判别提供了简单有效的手段。应用实例表明了奇异摄动时滞不确定系统鲁棒稳定性充分条件使用的方便性。     

Robust Control for a Class of Time-delay Nonlinear Systems via Output Feedback Strategy

This paper studies the robust control problem for time-delay systems with complicated inherent nonlinearities and unknown disturbances. Based on the modified homogeneous domination method and by constructing the proper Lyapunov-Krasovskii (L-K) functional, output feedback controllers are successfully constructed to guarantee the boundedness of all the states of the closed-loop system. The convergence of the states is also realizable when the L₂ norm of the disturbance exists. The presented method is also extended to solve the control problem of nonholonomic time-delay system. Simulation examples are given to show the effectiveness of the proposed theory.     

线性二次型最优控制闭环系统极点的必要条件

本文推导了线性二次型(LQ)最优控制闭环系统极点应满足的必要条件,以及与加权阵Q和R的等式关系。     

Polynomial Design of Optimal Sampled-Data Tracking Systems I. Quadratic Optimization

A method of optimal design of digital tracking systems for continuous-time plants is presented. The method is based on the use of Laplace transformation in continuous time and polynomial equation theory. The cost function employed for quadratic optimization takes system performance in continuous time into account. The structure of optimal digital controller transfer function is investigated and its order is determined explicitly. The possibility of designing optimal tracking system for a neutral plant is analyzed.     

Analysis of Polynomial Systems With Time Delays via the Sum of Squares Decomposition

We present a methodology for analyzing robust independent-of-delay and delay-dependent stability of equilibria of systems described by nonlinear Delay Differential Equations by algorithmically constructing appropriate Lyapunov-Krasovskii functionals using the sum of squares decomposition of multivariate polynomials and semidefinite programming. We illustrate the methodology using an example from population dynamics.      

一类不确定模糊系统的二次稳定性问题的研究

基于T-S模糊模型研究了一类非线性连续不确定时滞系统的二次稳定性问题。给出了使系统二次稳定的模糊状态反馈控制器存在的充分条件,该充分条件以线性矩阵不等式的形式给出,因而具有数值易解性。     

Stability of Hybrid Impulsive and Switching Stochastic Systems with Time-delay

This paper investigates a model of hybrid impulsive and switching stochastic systems (HISSS) with time-delay. Several stability criteria, including the globally asymptotical and exponential stability criteria in the pth moment and mean square, are established by using Itô formula, a generalized switching Lyapunov functions and some relating techniques. Especially, a more general Lyapunov-Krasivskii functional is constructed, and it is observed that the mean square asymptotic and exponential stability conditions of HISSS are delay-dependent. A numerical example shows that the obtained stability results can reduce the conservativeness.     

Stabilization of Switched Systems via Composite Quadratic Functions

This paper investigates stabilization of switched systems by using a Lyapunov function composed of a family of continuously differentiable functions. Switching laws are constructed by using the directional derivatives along the trajectories of the subsystems. Conditions for stabilization are established with careful consideration of sliding modes and directional derivatives along sliding modes. Three types of composite quadratic Lyapunov functions, the max of quadratics, the min of quadratics and the convex hull of quadratics are used for deriving matrix conditions of stabilization and for constructing switching laws. Dual stabilization results are established with respect to the pair of conjugate Lyapunov functions: the max of quadratics and the convex hull of quadratics. Conditions of stabilization are derived as bilinear matrix inequalities and solved with LMI-based numerical tools. Relationship between the newly derived conditions and some existing conditions are investigated. It is observed that the min of quadratics, which is nondifferentiable and nonconvex, may be a more convenient tool than the other two types of functions which are convex and/or differentiable. Numerical examples are used to demonstrate the synthesis results and the advantage of the composite quadratic functions over existing multiple Lyapunov functions. In particular, better results have been obtained when the number of quadratic functions is greater than the number of subsystems.      

Exponential Stability of Interval Dynamical Systems with Quadratic Nonlinearity

This article proposes an approach for investigating the exponential stability of a nonlinear interval dynamical system with the nonlinearity of a quadratic type on the basis of the Lyapunov’s direct method. It also constructs an inner estimate of the attraction domain to the origin for the system under consideration.     

Input-to-State Stability for Nonlinear Time-Varying Systems via Averaging

 We introduce two definitions of an averaged system for a time-varying ordinary differential equation with exogenous disturbances (“strong average” and “weak average”). The class of systems for which the strong average exists is shown to be strictly smaller than the class of systems for which the weak average exists. It is shown that input-to-state stability (ISS) of the strong average of a system implies uniform semi-global practical ISS of the actual system. This result generalizes the result of [TPA] which states that global asymptotic stability of the averaged system implies uniform semi-global practical stability of the actual system. On the other hand, we illustrate by an example that ISS of the weak average of a system does not necessarily imply uniform semi-global practical ISS of the actual system. However, ISS of the weak average of a system does imply a weaker semi-global practical “ISS-like” property for the actual system when the disturbances w are absolutely continuous and . ISS of the weak average of a system is shown to be useful in a stability analysis of time-varying cascaded systems. Date received: April 6, 1999. Date revised: April 11, 2000.     

一类模糊时滞系统输出跟踪控制

基于T-S模糊模型和变结构控制策略,研究了一类带有参数不确定项的模糊时滞系统输出跟踪问题。利用变结构控制理论选择滑动模,针对系统时滞项为已知和未知的两种情况,根据可达条件提出了一种变结构控制方法。该方法确保系统的运动轨迹在有限的时间内到达滑模面并一直保持在滑模面上。根据ISS理论和LMI方法研究了系统状态全局有界的充分条件。通过仿真实例验证了所提方法的正确性和有效性。