非线性齐次时滞系统H_∞控制

讨论了非线性齐次时滞系统的H∞控制问题.首先给出了非线性仿射齐次时滞系统的Lyapunov泛函V(x)具体形式,选取适当的λ* ,使得当λ>λ*时系统的Hamilton-Jacobi-Isaacs不等式有解,从而解决了系统的L2 增益问题.文章最后构造了具体状态反馈控制律u(x) ,使时滞Lyapunov泛函V(x)沿闭环系统轨线导数小于零,保证了系统的渐进稳定性,因而解决了系统的H∞控制问题.     

随机泛函微分方程正整体解的存在唯一性及矩有界性

构造了Lyapunov函数V (x),然后给出一个一般条件,应用Khasminskii?Mao定理,得到非线性随机泛函微分方程(SFDEs)存在正整体解,且这个解p阶矩有界.     

基于模糊系统的非线性连续系统自适应调节器

对于一类连续时间的非线性动态系统 x=f (x) Bu d,当系统中的非线性函数 f (x)满足线性增长条件时 ,首先证明 f (x)中的 x落入一紧集中 ,然后根据模糊系统的逼近性质 ,给出自适应调节器的设计方法。利用李亚普诺夫方法证明控制算法是全局稳定的 ,闭环系统的状态是一致最终有界的。     

方程(dx-dt=(ψ)(y)-F(x),dy-dt=h(x,y)-g(x))的极限环存在定理

在不同的区域上构造适当的比较函数,将Filippov定理推广到更一般的非线性系统(dx-dx==(ψ)(y)-F(x),dy-dt=h(x,y)-g(x)).     

具有渐进非线性项的Kirchhoff型方程的正解（英文）

本文研究一类非线性Kirchhoff型方程.非线性项函数f(x, u)在无穷远处关于u是渐进线性或渐进非线性的.若位势函数V (x)和非线性项f(x, u)满足给定的条件,本文在工作空间缺乏紧性嵌入的情形下获得该方程正解的存在性.     

关于一类三阶非线性系统的全局渐近稳定性

本文考虑三阶非线性系统 x=y-h(x),y=φ(z)-g(x),z=-f(x) (1) 这里g(x)为连续函数,h(x),φ(z),f(x)为连续可微函数。我们改进文[4]中的结果,证明了如下的结论:     

一类三阶非线性系统的全局渐近稳定性

对一类三阶非线性系统构造出了较好的Lyapunov函数,得到其零解全局渐近稳定的充分性准则,而且去掉了一般要求Lyapunov函数具有无穷大这个较强的条件,只要求系统正半轨线有界,所得结果包含并改进了旧有的结果.     

非线性矩阵微分系统的h稳定性

讨论了一类非线性矩阵微分系统,运用Lyapunov函数法和Kronecker积给出了非线性矩阵微分系统h稳定性的若干判断准则.     

一类具有两个非线性项的四阶非线性系统的稳定性

利用"类比法"构造了一类四阶非线性系统的Lyapunov函数,给出了该系统零解稳定性的充分条件.     

关于非线性过程最优控制的存在性问题

本文讨论了形为x=f(t,x,u)的系统的最优控制的存在性问题,f(f,x,u)是比较一般的非线性函数,控制类普遍到足以包含一般工程上常见的控制函数.还讨论了由属于一定函数类的控制函数序列去逼近最优控制的问题,举出了与文[1]结论相矛盾的反例,并导出这问题的正确结论.     

Optimizing Lyapunov functions for systems with structured uncertainties

The robust stability problem of a nominally linear system with nonlinear, time-varying structured perturbationsp _j ,j=1,...,q, is considered. The system is of the form $$\dot x = A_N x + \sum\limits_{j = 1}^q {p_j A_j x} .$$ When the Lyapunov direct method is utilized to solve the problem, the most frequently chosen Lyapunov function is some quadratic form. The paper presents a procedure of optimization of Lyapunov functions. Under some simple conditions, the weak convergence of the procedure is ensured, making the procedure effective in solving the robust stability problem. The procedure is simple, requiring only numerical routines such as inverting positive-definite symmetric matrices and determining the eigenvalues and eigenvectors of symmetric matrices. It is expected that the optimal Lyapunov function may be used in a robust linear feedback controller design. The examples demonstrate the effectiveness of the method. As shown when considering a system of dimension 24, the method is effective for large-scale systems.     

On the Robust Practical Global Stability of Nonlinear Time-varying Systems

The goal of this paper is twofold. The first part presents a Lyapunov statement and proof of the concept of robust global practical exponential stability (RpGES) for nonlinear time varying systems. A RpGES-Lyapunov function for the overall system is exhibited. Its proof is a consequence of some results on converse Lyapunov theorems obtained by Tsinias in 19. The second part provides sufficient conditions for the robust practical globally uniformly asymptotically stability (RpGUAS).     

On stability of switched homogeneous nonlinear systems

In this paper, the problem of stability of switched homogeneous systems is addressed. First of all, if there is a quadratic Lyapunov function such that nonlinear homogeneous systems are asymptotically stable, a matrix Lyapunov-like equation is obtained for a stable nonlinear homogeneous system using semi-tensor product of matrices, and Lyapunov equation of linear system is just its particular case. Following the previous results, a sufficient condition is obtained for stability of switched nonlinear homogeneous systems, and a switching law is designed by partition of state space. In particular, a constructive approach is provided to avoid chattering phenomena which is caused by the switching rule. Then for planar switched homogeneous systems, an LMI approach to stability of planar switched homogeneous systems is presented. Similar to the condition for linear systems, the LMI-type condition is easily verifiable. An example is given to illustrate that candidate common Lyapunov function is a key point for design of switching law.     

Global stability of coupled nonlinear systems with Markovian switching

This paper investigates the global stability of a coupled nonlinear system with Markovian switching (CNSMS), which can be described in a graph. A theoretical framework for the construction of Lyapunov function for the CNSMS is derived in a combined method of graph theory and Lyapunov function. Furthermore, we obtain a global stochastic asymptotical stability principle, which has a close relation to the topology property of the graph. Finally, to illustrate the capabilities of the principle, the stochastic stability of a coupled oscillator system is investigated.     

Vector Wirtinger-type inequality and the stability analysis of delayed neural network

This paper proposes some new stability criteria for a class of delayed neural networks with sector and slope restricted nonlinear neuron activation function. By using the convex express of the nonlinear neuron activation function, the original delayed neural network is transformed into a linear uncertain system. The proposed method employs an improved vector Wirtinger-type inequality for constructing a novel Lyapunov functional. Based on the Lyapunov stable theory, new delay-dependent and delay-independent stability criteria for the researched system are established in terms of linear matrix inequality technique, delay partitioning approach and characteristic root method. Three illustrative examples are presented to verify the effectiveness of the main results.     

LMI based design of constrained fuzzy predictive control

Predictive control of nonlinear systems subject to output and input constraints is considered. A fuzzy model is used to predict the future behavior. Two new ideas are proposed here. First, an added constraint on the applied control action is used to ensure the decrease of a quadratic Lyapunov function, and so guarantee Lyapunov exponential stability of the closed-loop system. Second, the feasibility of the finite-horizon optimization problem with the added constraints is ensured based on an off-line solution of a set of LMIs. The novel stability method is compared to the existing methods, such as the techniques based on the end-point constraints (terminal constraint set), and the robust stability techniques based on the small gain theory. The proposed method ensures Lyapunov exponential stability, does not need an auxiliary controller and can be used with any feasible controller parameters. Illustrative examples including the predictive control of a highly nonlinear chemical reactor (CSTR) are discussed.     

On the use of a general quadratic Lyapunov function for studying the stability of Takagi–Sugeno systems

We study the stability of the zero solution to a nonlinear system of ordinary differential equations on the base of its Takagi–Sugeno (TS) representation. As is known, the most constructive stability and stabilization conditions for TS systems stated as linear matrix inequalities are established with the help of a general quadratic Lyapunov function (GQLF). However, such conditions are often too rigid. Using a modification of the Lyapunov direct method, we propose asymptotic stability conditions with weaker requirements to GQLF. They allow an application to a wider class of systems. We also give some illustrative examples.     

Analysis of a set of nonlinear dynamics trajectories: Stability of difference equations

For a set of difference equations generated by discretization of the set of differential equations with Hukuhara derivative a principle of comparison with matrix Lyapunov function is specified and sufficient stability conditions of certain type are established. The analysis is carried out in terms of a matrix Lyapunov function of special structure. For an essentially nonlinear multiconnected switched difference system, conditions are obtained providing the asymptotic stability of its zero solution for any switching law. An example is presented to demonstrate efficiency of the proposed approaches.