时滞离散广义大系统的稳定性分析

从时滞离散广义大系统的满足容许条件的孤立子系统出发,利用李雅普诺夫方法,通过对关联矩阵、输入矩阵和非线性项加上范数有界约束条件,分别研究了时滞离散广义大系统的线性情形和非线性情形的稳定性问题。给出了时滞离散广义大系统的线性情形和非线性情形的稳定性判据,并且得到了关联稳定参数域。最后用数值例子说明所得稳定性判据的实用性和有效性。     

一类非线性大系统的鲁棒反馈镇定控制器设计

通过对微分方程解的结构研究，运用比较原理和M－矩阵性质，建立了非线性关联子系统矩阵特征值与系统稳定性之间的关系，将一类复杂非线性系统的镇定问题转换成经典的特征值配置问题，文章仅需假定系统的非线性（可能含不确定性）成分具范数界，不必要求其范数满足匹配条件，所给出的方法为实际控制系统的工程设计提供了一套较完整的符合性能要求的镇定控制器算法。     

一类非线性级联系统的鲁棒不变切换控制

研究了一类具有结构不确定性的单输入非线性级联系统的鲁棒不变切换控制问题。通过基于鲁棒严格无源技术和线性子系统状态反馈的切换控制来镇定线性子系统,同时保证了指定区域的正不变性,从而得到了该类系统鲁棒不变切换控制的充分条件。在适当的假设下,得到了系统的半全局渐近稳定。设计中无需ISS假设或非线性项的线性增长条件假设。在MATLAB环境下的仿真结果表明了设计的有效性。     

一类多输入非线性系统的切换控制

研究了一类具有结构不确定性的多输入非线性级联系统的鲁棒不变切换控制问题.控制思想是首先通过鲁棒无源性技术来镇定线性子系统,再借助切换控制技术得到系统轨迹对于指定区域的正不变性,从而得到了该类系统鲁棒不变切换控制的充分条件.在适当的假设下,得到了系统的半全局渐近稳定.设计中无需ISS假设或非线性项的线性增长条件假设.仿真表明了设计方法的有效性.     

二阶输出反馈滑模极值搜索控制方法

针对一类单输入单输出(single input single output,SISO)非线性极值系统的控制问题,提出了一种二阶输出反馈滑模极值搜索控制方法。考虑到此系统的状态量不可测,利用斜坡函数作为输出量的参考跟踪信号,以系统的输出跟踪误差及其微分信号构建切换函数,设计出二阶滑模极值搜索控制律。稳定性分析证明了在任意初始条件下,该方法可使系统的输出量全局收敛至其期望极值的任意小邻域内且所有状态量均是一致范数有界。仿真结果验证了该方法的有效性。     

一类非线性切换系统观测器设计的新方法

针对一类切换规则为时间依赖型的Lipschitz非线性切换系统,采用驻留时间方法研究了状态观测器设计问题.该切换系统同时含有可观测子系统与不可观测子系统,通过构造合适的Lyapunov函数,并利用矩阵不等式技术得到了保证状态观测器状态估计误差收敛的条件.并给出了观测器设计步骤.进一步,通过矩阵变换将观测器增益求解转化为LMI形式.最后给出了仿真算例说明了该设计方法的有效性.     

非线性中立型控制系统的鲁棒稳定与鲁棒镇定

研究了一类不确定性的非线性中立型动态系统,系统具有多重时不变状态时滞。其不确定性满足范数有界条件。采用LyapunovV泛函的方法。建立了一类Lyapunov泛函。通过对控制系统(B,D,C)的分析,得出只要矩阵对(B,D)是完全可控的,或者是可稳定的,则在相应的条件下便得出相应的非线性中立型动态控制系统及滞后型动态系统可镇定的充分条件。建立了非线性中立型微分系统的时滞无关的渐近稳定性判别条件,以及非线性中立型动态控制系统的时滞无关鲁棒镇定的判据。同时,给出了相应的非线性滞后微分系统的时滞无关鲁棒稳定性的判据,以及非线性滞后动态控制系统的时滞无关鲁棒镇定性的代数判据。     

一类大型互联非线性时滞系统的鲁棒控制

对一类大型互联非线性不确定时滞系统进行了分散状态反馈控制设计。通过子系统状态的线性变换,得到分散状态反馈控制律。当状态反馈控制律作用于该系统时,闭环系统是全局一致渐近稳定的,且控制器的设计无需解任何的矩阵不等式,并给出仿真算例说明该结论的可行性和有效性。     

一类切换系统的鲁棒状态反馈控制

考虑了一类非线性不确定切换系统的鲁棒状态反馈稳定问题，不确定项包含了系统矩阵的摄动以及满足匹配条件和不满足匹配条件三部分．对于给定的不确定切换系统，研究了其二次稳定和渐近稳定问题．基于公共李雅普诺夫函数方法，以矩阵不等式的形式给出了非线性切换系统鲁棒状态反馈稳定的若干充分条件．仿真结果验证了文中结论的正确有效性。     

多输入多输出网络控制系统的绝对稳定性分析

考虑到网络诱导时延和网络通道的非线性反馈干扰,研究了多输入多输出网络控制系统的时滞依赖稳定性。基于各回路有界的状态反馈输入,建立闭环系统的Lurie时滞系统模型。应用Lyapunov稳定性理论和线性矩阵不等式工具,分析了各子系统在有扇形条件约束的绝对稳定性,同时得到网络控制系统全局稳定运行的最大允许时延界。最后,通过仿真例子,表明该方法是可行的。     

不确定切换组合大系统的鲁棒分散控制

考虑了一类不确定切换组合大系统的鲁棒分散状态反馈镇定问题。利用单李雅普诺夫函数方法,得到了不确定切换组合大系统鲁棒可稳的充分条件。在互相关联的低维子系统的状态矩阵和控制输入矩阵同时带有未知、时变但有界的不确定性、各自的单个子系统均不能被镇定的情况下,基于凸组合技术和线性矩阵不等式方法,设计出分散状态反馈控制器及相应的分散切换策略,使得闭环系统渐近稳定。仿真结果表明所设计方法的正确有效性。     

时滞切换系统指数稳定性分析：Lyapunov-Krasovskii泛函方法

考虑由两个线性时滞子系统构成的切换系统,分析其在任意切换序列作用下保持指数稳定性的条件.分别利用二次型与逐段二次型的Lyapunov-Krasovskii泛函构造方式给出了以线性矩阵不等式所表述的稳定性判据;进而通过状态变量代换结合积分不等式技巧证明了指数衰减率对于所有切换序列一致成立,即其完全取决于系统的结构特征.最后给出了一个算例.     

Admissibility analysis and control synthesis for switched linear singular systems

The problem of admissibility analysis and control synthesis of discrete-time switched linear singular (SLS) systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities (LMIs). Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.     

Robust Finite-Time Stability and Stabilization of a Class of Fractional-Order Switched Nonlinear Systems

This paper deals with the problem of finite-time boundedness and finite-time stabilization boundedness of fractional-order switched nonlinear systems with exogenous inputs. By constructing a simple Lyapunov-like function and using some properties of Caputo derivative, the authors obtain some new sufficient conditions for the problem via linear matrix inequalities, which can be efficiently solved by using existing convex algorithms. A constructive geometric is used to design switching laws amongst the subsystems. The obtained results are more general and useful than some existing works, and cover them as special cases, in which only linear fractional-order systems were presented. Numerical examples are provided to demonstrate the effectiveness of the proposed results.     

Exponential stability of linear distributed parameter switched systems with time-delay

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.     

基于未知输入观测器方法的非线性切换系统故障检测

基于非线性未知输入观测器方法对一类离散时间非线性切换系统的故障检测问题进行了研究。给出了两种不同结构的非线性未知输入观测器。针对每一种观测器都考虑了两种切换信号:任意时间切换信号和满足平均驻留时间的切换信号。在任意切换信号下,使用了切换Lyapunov函数的方法来设计非线性未知输入观测器的参数;在满足平均驻留时间切换信号下,使用了多Lyapunov函数方法进行观测器参数的设计。然后利用已知的非线性未知输入观测器,得到残差生成器,进而实现故障检测。通过数值仿真例子,验证了故障检测方法的有效性。     

Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method

In this paper, the input-to-state stability (ISS) analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.     

Exponential stability of impulsive jump linear systems with Markov process

The exponential stability is investigated for a class of continuous time linear systems with a finite state Markov chain form process and the impulsive jump at switching moments. The conditions, based on the average dwell time and the ratio of expectation of the total time running on all unstable subsystems to the expectation of the total time running on all stable subsystems, assure the exponential stability with a desired stability degree of the system irrespective of the impact of impulsive jump. The uniformly bounded result is realized for the case in which switched system is subjected to the impulsive effect of the excitation signal at some switching moments.     

一类不确定时滞非线性系统的H∞鲁棒镇定

利用混杂状态反馈策略研究一类不确定时滞非线性系统的鲁棒H_∞镇定问题.首先,当控制器增益矩阵均已知时,利用单Lyapunov函数法和凸组合技术,给出了闭环非线性切换系统具有鲁棒H_∞性能的充分条件并设计出相应切换律.然后,当控制器增益矩阵均未知时,利用多Lyapunov函数法,设计了控制器及相应的切换策略,使闭环非线性切换系统是鲁棒H_∞渐近稳定的.