2-D unitary matrix pencil method for efficient direction of arrival estimation

In this study, we extended the one-dimensional (1-D) unitary matrix pencil method (UMP) [N. Yilmazer, J. Koh, T.K. Sarkar, Utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival, IEEE Trans. Antennas Propagat. 54 (1) (2006) 175–181] to two-dimensional case, where 2-D matrix pencil (MP) method are used to find the 2-D poles corresponding to the direction of arrival (DOA), azimuth and elevation angles, of the far field sources impinging on antenna arrays. This technique uses MP method to compute the DOA of the signals using a very efficient computational procedure in which the complexity of the computation can be reduced significantly by using a unitary matrix transformation. This method applies the technique directly to the data without forming a covariance matrix. Using real computations through the unitary transformation for the 2-D matrix pencil method leads to a very efficient computational methodology for real time implementation on a DSP chip. The numerical simulation results are provided to see the performance of the method.     

矩阵束的稳定凸组合与完备性的等价关系

矩阵束存在稳定凸组合是其有分段公共Lyapunov函数的一个充分条件．矩阵束的完备性是切换系统为稳定且存在切换控制函数一个充分条件．本文讨论了在一定条件下矩阵束稳定凸组合的存在性和相应矩阵束的完备性的等价关系，给出切换系统的分段Lyapunov函数的构造方法．并分析了自治切换系统的稳定性。     

具有时变状态滞后的非线性2-D 离散系统的稳定性与控制

考虑一类由局部状态空间Fornasini-Marchesini(FM LSS)第二模型描述的,具有时变状态滞后非线性二维(2-D)离散系统的稳定性分析和控制问题.时变状态滞后项的上、下界为正整数,非线性项满足Lipschitz条件.首先,通过引入一个含有时滞上、下界的新Lyapunov函数,给出了系统的稳定性准则;然后设计了状态反馈控制器以保证系统的稳定性,进而,状态反馈控制律可由线性矩阵不等式求得;最后通过数值算例表明了所得结果的有效性.     

一般2-D线性常系数离散状态空间模型渐近稳定性的一类Lyapunov方法

本文给出了一般2-D线性常系数离散状态空间模型(2-D GM)的渐近稳定性的定义以及相应的判据,并借助于Lyapunov方程给出了2-D Roesser Model(2-D RM)渐近稳定条件,推广和简化了文献[1,7]的有关结论。最后通过行列式的一个简单性质,证明了关于2-DGM渐近稳定性的判定可以转化为一类特殊的2-D RM的相应问题,从而得到了判定2-D GM渐近稳定性的Lyapunov方法。     

具有时变状态滞后2-D离散系统的稳定与镇定(英文)

针对一类由局部状态空间(LSS)Fornasini-Marchesini(FM)第二模型描述的,具有时变状态滞后的2-D离散系统,其中时变滞后项的上、下界均为正实数,研究了其稳定性和控制综合问题。首先,利用Lyapunov-Krasovski泛函方法,提出了系统的稳定性准则。再根据这一准则,分别设计状态反馈和动态输出反馈控制器保证系统的稳定性。状态反馈控制律和输出反馈矩阵可由线性矩阵不等式(LMI)求得。最后,通过数值算例说明所得结果的有效性。     

Stability analysis of two-dimensional systems by means of finitely constructed bilateral quadratic forms

Asymptotic stability of two-dimensional (2-D) systems in the state-space representation is studied. The concept of finitely constructed bilateral quadratic forms is introduced for the set of bilateral sequences of vectors, and the positivity of a bilateral quadratic form is characterized in terms of the solvability of an algebraic Riccati matrix inequality. A Lyapunov-like stability analysis of 2-D systems is conducted by resorting to positivity tests for a sequence of bilateral quadratic forms generated by a recurrence formula. The effectiveness is proved in an illustrative example.     

Matrix pencil characterizations of disturbance decoupling for systems with direct feedthrough matrices

In this paper new necessary and sufficient conditions are given for the disturbance decoupling problem with or without stability and pole placement for linear time-invariant systems with direct feedthrough matrices, based on matrix pencil theory. All results are proved on the basis of a condensed form that can be computed using orthogonal matrix transformations, i.e., transformations that can be implemented in a numerically stable way.     

离散区间2-D系统的鲁棒稳定性

基于第2类Fornasini-Machesini模型,研究离散区间2-D系统鲁棒稳定的问题.引入区间不确定性,建立离散区间2-D系统数学模型,根据2-D系统渐近稳定的一种Lyapunov不等式判据和一个对称区间矩阵正定性引理,给出离散区间2-D系统鲁棒稳定的一个充分条件,并通过数值算例表明所给出的离散区间2-D系统鲁棒稳定的充分条件是有效的.     

2-D系统的稳定性问题

以线性矩阵不等式为工具,研究有关2-D系统第二类Fornasini-Marchesini模型的稳 定性的问题.首先提出了该类系统的一种Lyaptunov不等式,由此给出了该类系统渐近稳定的新 的判别条件.其次,给出了该类系统能稳定化的充分条件和反馈矩阵的求法.最后,提出了一种 求该类系统的稳定性裕度下界的方法,并指出了利用该方法得到的稳定性裕度的下界大于原有 文献中给出的下界.     

Stability of nonlinear parameter-varying digital 2-D systems

A general state-space model for nonlinear parameter-varying digital two-dimensional (2-D) systems is proposed. Sufficient conditions for system stability are given. Presented theorem can be considered as a generalization of the Lyapunov stability theorem for one-dimensional nonlinear systems. Given results can be useful in stability analysis for systems described by 2-D models     

一类存在数据丢失二维离散系统的H∞滤波

研宄输出测量数据丢失情况下二维线性离散系统的H_∞。滤波问题.首先,将数据丢失现象描述为随机伯努利序列,在此基础上建立二维系统状态估计误差的随机动态方程.其次,定义随机意义下的二维系统均方渐近稳定性和H_∞。性能,基于线性矩阵不等式给出误差系统满足均方渐近稳定和H_∞。性能的一个充分条件,该条件可以实现滤波器参数矩阵的设计.同时,研宄结果被进一步推广到不确定二维系统.最后,通过仿真示例验证了理论结果的有效性.     

关于可分2－D系统的几个注记

可分２－Ｄ系统是一类具有良好特性的重要的特殊２－Ｄ系统，它在多方面均有重要的应用．本文在已有结果的基础上对具有可分性的２－Ｄ多输入多输出系统在再实现问题、渐近稳定性代数判据、状态观测器设计等方面进行了较为广泛的研究，得到了许多较好的结果．     

关于可分2-D系统的几个注记

可分２－Ｄ系统是一类具有良好特性的特殊２－Ｄ系统，它在多方面均有重要的应用。本文在已有结果的基础上对具有可分性的２－Ｄ多输入多输出系统的再实现问题、渐近稳定性代数判据、状态观测设计等方面进行了较为广泛的研究，得到了许多较多的结果。     

On the stability of linear systems with uncertain delay

This paper focuses on the stability of some class of delay systems, including uncertainty in the delays. More precisely, we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system. If the delay perturbation is constant, necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some (finite-dimensional) constant matrix pencil. If the delay perturbation is time-varying, some sufficient stability conditions are derived using "exact" Lyapunov-Krasovskii functionals. Illustrative examples are also included.     

具有区间时变时滞2-D 离散系统的时滞相关稳定与控制

针对具有区间时变时滞2-D离散系统,利用时滞相关方法,研究其稳定性与控制问题.首先选取含有时滞项上、下界的一个新的Lyapunov函数,对其差分时考虑所有项,得到了基于线性矩阵不等式(LMI)的时滞相关稳定性准则;然后给定时变时滞项的下界,再由一个凸优化问题最大化其上界,进而通过状态反馈实现系统的时滞相关控制,且求解LMI可得到增益矩阵;最后,利用数值算例说明了所得结果有效且优于已有成果.     

An LMI based criterion for the global asymptotic stability of 2-D discrete state-delayed systems with saturation nonlinearities

This paper deals with the problem of global asymptotic stability of a class of two-dimensional (2-D) discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model in presence of saturation nonlinearities and state delays in each of the two independent directions of information propagation. A linear matrix inequality (LMI) based criterion for the global asymptotic stability of such systems is presented. It is shown that several previously reported stability criteria for 2-D discrete FMSLSS model with saturation nonlinearities are recovered from the presented approach as special cases.     

Noninteracting control of 2-D systems

Necessary and sufficient conditions for the existence of a decoupling bicausal precompensator for multivariable 2-D systems are derived in state-space and frequency domains. In general, the decoupling problem for 2-D systems can be solved by feedback compensators if suitable injectivity assumptions are introduced on the input-state matrices. The structure of dynamic compensators is derived for this case, and the 2-D decoupling problem with stability is solved     

不确定线性2-D 离散系统的鲁棒滑模控制

针对不确定线性离散二维（2-D）系统,研究了其鲁棒稳定性、鲁棒镇定和鲁棒滑模控制问题.基于线性矩阵不等式的方法推导了该系统鲁棒渐近稳定的充分条件,并给出了系统状态反馈镇定器和理想滑动模态存在的充分条件.改进了离散时间滑模控制系统的趋近律方法,使得状态能够到达滑模面上产生理想的滑动模态,并将其推广应用到2-D离散系统中,综合了一类滑模控制器保证闭环系统鲁棒渐近稳定.仿真实例证实了该设计方法的有效性.     

Analysis and control of the jump modes behavior of 2-D singular systems—Part I: Structural stability

This paper considers the problem of structural stability of 2-D singular systems. Firstly, some properties of structural stability of 2-D general singular systems are presented. Sufficient and necessary conditions for the structural stability of the 2-D singular systems are given. Then, by extending the Lyapunov approach for the structural stability of 1-D continuous singular systems to the discrete case, a generalized Lyapunov equation approach to the analysis of the structural stability of 2-D singular Roesser models (2-D SRM) is proposed. The existence of a solution to the generalized Lyapunov equation gives a sufficient condition for the structural stability of the 2-D SRM.