区间矩阵稳定的充分条件

本文讨论了几类元素不确定区间矩阵的稳定性问题,得到了若干充分判据,改进了对称区间矩阵稳定性的结果。     

一类新的Takagi-Sugeno模糊时滞系统的稳定性准则

本文提出一种新的时滞划分方法—变时滞划分法,以解决连续延时Takagi-Sugeno模糊系统的稳定性和镇定性问题.不同于已有的文献,用可变参数将时变时滞区间[0,d(t)]划分为若干个可变子区间,并得出模糊时滞系统的新的时滞相关稳定性准则.本文提出的新方法能充分利用时滞子区间的内部信息,因此新的时滞相关稳定性准则比以往结果具有更小的保守性.基于Lyapunov稳定性理论,以线性矩阵不等式形式给出T--S模糊系统的新的时滞相关稳定性准则,并将稳定性和镇定性研究结果扩展到具有不确定参数的T--S模糊系统.仿真实例证明了本文方法降低保守性的有效性.     

带乘性噪声的非齐次Markov跳跃系统有限时间稳定性

研究一类带乘性噪声的离散时间非齐次随机Markov跳跃系统的有限时间稳定性,该系统的转移概率矩阵不是常矩阵而是区间矩阵.在区间矩阵紧性的假设下,将其表示为随机矩阵的凸组合.首先,给出系统有限时间稳定的充分必要条件;其次,利用Lyapunov方法和线性矩阵不等式技术得到系统有限时间稳定的充分条件,并用于设计有限时间状态反馈镇定控制器;最后,通过仿真算例说明所提出方法的有效性.     

关于区间矩阵的稳定性

文献[1]试图给出由端点矩阵的稳定性来保证区间矩阵的稳定性,文[2,3]指出文[1]的主要结果是错的.本文给出了端点矩阵的稳定性在一定条件下可以保证区间矩阵的稳定性,其结果比文[4]更精确,适用范围更大,且对具有分解的区间矩阵给出了其稳定及不稳定的充分条件.     

带有时滞的区间动力系统的鲁棒稳定性研究

给出了区间动力系统稳定性的相关概念,讨论了带有时滞的区间动力系统的鲁棒稳定性.通过构造控制矩阵和迭代相结合的方法,给出了一类带有时滞的区间动力系统鲁棒稳定的判别方法,并且给出了系统鲁棒稳定时参数取值的最大区间.将含有时滞的区间动力系统的稳定性转化为判别一个矩阵的稳定性,推广和改进了已有的结论.     

区间矩阵稳定的充分条件

讨论几类区间矩阵的稳定性，仅用区间矩阵元素的简单关系，获得了几个新的简单实用的充分条件。     

一类不确定系统的鲁棒稳定性分析

研究了一类不确定系统的稳定性问题, 以线性矩阵不等式(LMI)的形式给出了该类系统的鲁棒稳定条件, 并将该结果推广到区间系统的稳定性分析, 提出了研究区间系统稳定性问题的新方法, 给出了线性矩阵不等式形式的稳定判据, 该判据将区间系统的稳定性问题转化为一类线性矩阵不等式的可解问题. 最后通过仿真算例验证了本文结果具有更小的保守性.     

广义区间动力系统的稳定性分析

考虑广义区间动力系统的稳定性问题 .利用矩阵测度的有关性质 ,得到了广义区间动力系统稳定的充分条件 ,该充分条件保证所考虑的广义区间动力系统正则 ,无脉冲且稳定 .     

一种改进的区间时变时滞系统稳定性准则北大核心CSCD

研究区间时变时滞系统的稳定性问题。首先,通过引入一个区间调节参数,将系统时滞区间分解为两部分之和。其次,在两个子区间的基础上构造一个包含更多时滞信息和三重积分项的新Lyapunov-Krasovskii (L-K)泛函。在处理来自L-K泛函求导过程中产生的积分交叉项时,将时滞分属于各子区间的情况作为一个整体来研究。然后,基于Lyapunov稳定性理论,以线性矩阵不等式的形式给出一个新的稳定性准则。最后,通过两个数例证明所得稳定性准则的有效性。     

具有多个执行机构的Lurie控制系统的鲁棒稳定性

具有多个执行机构的Ｌｕｒｉｅ控制系统的鲁棒稳定性年晓红（湘潭工学院自动化工程系湘潭４１１２０１）关键词区间矩阵，区间直接控制系统，区间间接控制系统，绝对稳定性．Ｌｙａｐｕｎｏｖ函数．收稿日期１９９６－０４－０１１引言具有多个执行机构的Ｌｕｒｉｅ型控制...     

Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACT

This paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.     

Controllability and observability of linear time-invariant compartmental models

The problems of complete controllability and complete observability of linear time-invariant compartmental models with general input-output structures are considered. The analysis of these problems is based largely on graph-theoretic methods and the properties of polynomial matrices. Specifically, statements on complete controllability and complete observability are proven by using graphical constructions which do not change the basic properties of controllability and observability. The major results of this paper are: 1) A unique decomposition of the digraph of a compartmental model into sources, sinks, and transits. 2) A theorem which states that a compartmental model with closed sinks is completely observable if and only if the matrix [C^{T}, A^{T}] is full rank, and a corollary which provides a sufficient condition for complete observability of all other linear time-invariant compartmental models. 3) A theorem which states that a single sink compartmental model is completely controllable if and only if a compartment from each source is controlled. 4) A controllability algorithm which provides sets of excitations which are sufficient for complete controllability of any linear time-invariant compartmental model.     

New necessary and sufficient conditions for local controllability and local observability of 2-D separable denominator systems

New necessary and sufficient conditions for local controllability and observability of 2-D separable denominator systems (SDS's) are presented on the basis of the reduced-dimensional decomposition of 2-D SDS's. It is proved that local controllability of a 2-D SDS is equivalent to controllability of two 1-D systems which are a special decomposition pair of the 2-D SDS. Furthermore, local observability of a 2-D SDS is equivalent to a full rank condition of the coefficient matrices of the 2-D SDS in addition to observability of two 1-D systems which are another special decomposition pair of the 2-D SDS. Thus, these new conditions which use only 1-D controllability matrices, 1-D observability matrices, and coefficient matrices of the 2-D SDS are much simpler than any previous conditions which use complex 2-D controllability and observability matrices.     

Reachability matrix and relation to large-scale systems

A sequential derivation of the reachability matrix is given, related to graph theoretic considerations, and earlier results on the structural inverse of a matrix are reformulated on the basis of an observed duality. A relationship between a matrix, a full rank permutation matrix included in it and its reachability matrix are given, as well as a property of the reachability matrix of a product. A hypothesis on the reachability matrix, stating that it is ‘its own inverse’ and relating to the structural modal matrix, is confirmed and the reachability and the acyclic input-output reachable partitions of dynamic systems are discussed; forms relating them to structural controllability, structural observability and structural transfer function matrices are presented.     

Frequency Interval Cross Gramians for Linear and Bilinear Systems

In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian‐based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians relative to existing methods.     

The Controllability,Observability, and Stability Analysis of a Class of Composite Systems with Fractional Degree Generalized Frequency Variables

This paper is concerned with fundamental properties of a class of composite systems with fractional degree generalized frequency variables, including controllability, observability and stability. Firstly, some necessary and sufficient conditions are given to guarantee controllability and observability of such composite systems. Then we prove that the stability problem of such composite systems can be reduced to judging whether a fractional degree polynomial is stable. Finally, the stability analysis result is applied in the supervisory control of fractional-order multi-agent systems, and an example is provided to illustrate the effectiveness of the proposed methods.      

Controllability and observability of switched multi-agent systems

This paper considers controllability and observability of switched multi-agent systems, which are composed of continuous-time and discrete-time subsystems. First, a controllability criterion is established in terms of the system matrices. Then, by virtue of the concepts of the invariant subspace and the controllable state set, a method is proposed to construct the switching sequence to ensure controllability of switched multi-agent systems, and a necessary and sufficient condition is obtained for controllability. Moreover, a necessary controllability condition is derived in terms of eigenvectors of the Laplican matrix. With respect to observability, two necessary and sufficient algebraic conditions are obtained. Finally, simulation examples are provided to illustrate the theoretical results.     

New results in stability of a class of hereditary linear systems

Some basic connections between bounded-input, bounded-output stability and exponential asymptotic stability are presented for a class of linear time-varying hereditary systems. For that class of systems, controllability and observability are closely related to that of an equivalent linear system. This eases the analytical treatment of such properties which are then used to derive the stability results. The requirement of boundedness of inputs and outputs in the BIBO definition is modified by requesting that their ‘energy content’ over a fixed-length interval should be bounded independently of the position of the interval. For the class of hereditary linear systems studied, it is found that EAS and BIBO stability are equivalent under uniform complete controllability and observability.     

Efficient algorithm for determining controllability and observability of large-scale composite systems

The investigation of controllability and observability of large composite systems requires the determination of the rank of large sparse matrices. A computationally efficient algorithm is presented, which is based on the application of reduced outer products for transforming the matrix into an upper triangular form.