Accelerating a recurrent neural network to finite-time convergence using a new design formula and its application to time-varying matrix square root

In this paper, a new design formula is presented to accelerate the convergence speed of a recurrent neural network, and applied to time-varying matrix square root finding in real time. Then, according to such a new design formula, a finite-time Zhang neural network (FTZNN) is proposed and investigated for finding time-varying matrix square root. In comparison with the original Zhang neural network (ZNN) model, the FTZNN model makes a breakthrough in the convergence performance (i.e., from infinite time to finite time). In addition, theoretical analyses of the design formula and the FTZNN model are provided in details. Comparative results further verify the superiority of the proposed FTZNN model to the original ZNN model for finding time-varying matrix square root.     

Exact Model-Matching of 2-D Systems via State Feedback

This paper considers the problem of matching the transfer function matrix of a given two-dimensional (2-D) system to that of a desired 2-D model using state feedback. The approach followed refers to systems having square transfer function matrices and reduces the problem to that of solving a linear system of equations. Furthermore, necessary and sufficient conditions are established for exact matching. An example is included to illustrate the proposed method.     

On a special form of the cauchy-schwarz inequality

This paper deals with questions concerning a transformation-based form of the Cauchy-Schwarz inequality (f,f)(g,g) ? (f,g)(g,f) where f and g are complex vectors. In the case of a linear transformation restricted to be real a refinement of the inequality can be given. The classes of transformation matrices are defined which impose the equality signs in the above inequalities and thus minimize their left hand sides. A diagonalization procedure provides the determination of a special canonical solution to the desired linear transformation and enables the explicit definition of the remaining degree of freedom.     

A Matrix Stability Criterion which does not Involve Forming the Characteristic Polynomial

A crucial problem in the theory of stability is to determine whether or not all of the eigenvalues of a system matrix have negative real parts. The classical test is to form the characteristic polynomial of the given matrix and then apply the Routh-Hurwitz criterion, which involves evaluating certain determinants. A new approach is presented in this paper; the characteristic polynomial is not formed, though certain differential equations must be integrated (numerically). Results of some computational experiments are encouraging.     

Parameter-dependent robust stability for uncertain Markovian jump systems with time delay

In this paper, the problem of parameter-dependent robust stability analysis is addressed for uncertain Markovian jump linear systems (MJLSs) with polytopic parameter uncertainties and time-varying delay. By constructing parameter-dependent Lyapunov functional, some sufficient conditions are developed to enable robust exponential mean square stability for the systems. New parameter-dependent robust stability criteria for MJLSs are established in the form of linear matrix inequalities (LMIs), which can be solved efficiently by the interior-point algorithm. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.     

An algorithm for Eigenvalue assignment in multi-input systems

This paper describes a computational method for solving the problem of eigenvalue assignment in a multi-input linear system. The given system is first reduced to an upper block Hessenberg form by means of orthogonal state coordinate transformations. It is then shown how a sequence of state feedback matrices and orthogonal state coordinate transformations can be applied to obtain a block triangular structure for the resulting state matrix, where the matrices on the diagonal are square matrices in upper Hessenberg form and of dimensions equal to the controllability indices of the multi-input system. Furthermore, the structure of the corresponding input matrix is such that the problem of eigenvalue assignment in the multi-input system can be reduced to several single-input eigenvalue assignment problems where the dimensions of the single-input systems are equal to the controllability indices of the multi-input system.     

Face-to-Face and Computer-Mediated Communities,A Comparative Analysis

In this article we combine the perspectives of sociology and computer science to compare face-to-face (f2f) and computer-mediated communications (CMC) from the viewpoint of their respective abilities to form and sustain communities. We also identify a third type of community-a hybrid-that is based on a combination of faceto-face (f2f) and CMC, or off- and online communications. The article thus in effect addresses an oft-asked question: Can virtual communities be "real", have the same basic qualities as f2f communities? The article is exploratory, because much of the necessary evidence has not yet been generated, and the relevant technologies are rapidly changing.     

Face-to-Face and Computer-Mediated Communities, A Comparative Analysis

In this article we combine the perspectives of sociology and computer science to compare face-to-face (f2f) and computer-mediated communications (CMC) from the viewpoint of their respective abilities to form and sustain communities. We also identify a third type of community-a hybrid-that is based on a combination of faceto-face (f2f) and CMC, or off- and online communications. The article thus in effect addresses an oft-asked question: Can virtual communities be "real", have the same basic qualities as f2f communities? The article is exploratory, because much of the necessary evidence has not yet been generated, and the relevant technologies are rapidly changing.     

Leaderless consensus of multi-agent systems via an event-triggered strategy under stochastic sampling

This paper investigates mean square leaderless consensus of networked nonlinear multi-agent systems. An efficient distributed event-triggered mechanism based on stochastic sampling is introduced to reduce the communication cost and controller updates. The stochastic sampling interval randomly switches between two given values. Mean square consensus criteria for multi-agent systems with strongly connected networks or networks containing directed spanning trees are derived, respectively. Moreover, the case with a special event-triggered weighting matrix and the case without even-triggered strategies are also discussed. Finally, an example is given to verify the theoretical results.     

Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems

This paper deals with the problem of non-fragile guaranteed cost control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are assumed to be time-varying and norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square for all admissible parameter uncertainties and the closed-loop cost function value is not more than a specified upper bound. A new sufficient condition for the existence of such controllers is presented based on the linear matrix inequality (LMI) approach. Then, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function. Numerical example is given to illustrate the effectiveness of the developed techniques.     

回归系数一类线性估计的小样本性质

提出了线性模型中回归系数的一类线性估计.在均方误差矩阵(MSEM)准则和Pitman Closeness(PC)准则下,研究了这类线性估计相对于最小二乘(LS)估计的优良性.最后,讨论了当设计阵为非列满秩时,回归系数的可估函数的一类线性估计的优良性.     

Overcoming backstepping limitations via a novel MIMO non-affine-in-control convex optimization technique

Limitations of the standard backstepping control technique are overcome in this paper by yielding global conditions for regional ones; specifically, flexible cascade arrangements that do not require the system to be put in a pure- or strict-feedback form to ensure controllability beforehand, handling of nonlinear MIMO blocks without invertible input distribution matrices, calculation of virtual and real control laws regardless of the non-affine-in-control nature of subsystems, and systematic numerical synthesis of Lyapunov-based control laws at each step of the cascade connection via linear matrix inequalities. All these benefits derive from exploiting exact convex rewriting of nonlinear terms, splitting available and non-available signals for control implementation, and applying the direct Lyapunov method to cast conditions as a convex optimization problem. Examples of academic and practical interest illustrate the advantages of the novel methodology over former approaches.     

Quantitative mean square exponential stability and stabilization of stochastic systems with Markovian switching

This paper is concerned with the quantitative mean square exponential stability and stabilization for stochastic systems with Markovian switching. First, the concept of quantitative mean square exponential stability(QMSES) is introduced, and two stability criteria are derived. Then, based on an auxiliary definition of general finite-time mean square stability(GFTMSS), the relations among QMSES, GFTMSS and finite time stochastic stability (FTSS) are obtained. Subsequently, QMSE-stabilization is investigated and several new sufficient conditions for the existence of the state and observer-based controllers are provided by means of linear matrix inequalities. An algorithm is given to achieve the relation between the minimum states’ upper bound and the states’ decay velocity. Finally, a numerical example is utilized to show the merit of the proposed results.     

基于DCT算法变换的图像压缩技术研究

离散余弦变换(DCT)是一种映射变换方法,通过把图像中的各个像素从一种空间变换到另一种空间,达到图像压缩的目的。本文对基于DCT变换的图像压缩方法进行了研究,给出了基于DCT变换的图像压缩的基本原理及其实现步骤,并最终给出了图像压缩结果。     

An Algorithm for Jordan Form Transformation

This paper presents a complete algorithm which transforms a square matrix into the Jordan normal form.     

On moment exponential stability of Markovian switching integral delay systems

This paper studies the moment exponential stability analysis of a class of Markovian switching integral delay systems (MSIDSs). The existence, uniqueness and stability of the solution are discussed firstly. Secondly, by selecting appropriate Lyapunov-Krasovskii (L-K) functionals, delay-dependent sufficient conditions are given such that the general form of MSIDSs and the special form of MSIDSs having multiple delays are mean square exponentially stable respectively. The results are then generalized to robust stability of MSIDSs having multiple delays with uncertain parameters. Finally, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.     

Co-design of transition rates and sliding mode switched controller for Markovian jumping systems under intermittent DoS attacks

This paper focuses on the stabilization problem for a class of Markovian jumping systems (MJSs) subject to intermittent denial-of-service (IDoS) attacks by synthesizing the sliding mode control (SMC) and the transition rate matrix (TRM). The existing conditions for the transition rates are firstly established to ensure the exponential mean-square stability of the unforced uncertain MJSs. And then, a co-design scheme for both the sliding mode controller and TRM is synthesized to achieve the exponential mean-square stability of the closed-loop system under IDoS, in which a switching estimator is utilized to estimate the unmeasurable system state. By introducing a novel Lyapunov function, both the reachability and the stability of sliding mode dynamics are detailedly analyzed, and an iterative optimization algorithm is given for solving the corresponding sufficient conditions. Finally, the proposed co-design SMC strategy is illustrated via the simulation examples.     

Absolute stability of uncertain discrete Lur’e systems and maximum admissible perturbed bounds

The robust absolute stability problem for norm uncertain and structured uncertain discrete Lur’e systems is considered in this paper by using Lyapunov function method. A sufficient condition of absolute stability for discrete Lur’e systems is established in terms of linear matrix inequalities (LMIs) or the equivalent frequency-domain condition. We compare the result with the Popov-like criterion (Tsypkin criterion) and extended strictly positive real (ESPR) lemma. Furthermore, sufficient conditions on absolute stability for discrete Lur’e systems with norm and structured uncertainties are also presented based on linear matrix inequalities. Estimates of the maximum bounds of all admissible perturbations are given by generalized eigenvalue problems. Finally, several numerical examples are worked out to illustrate the efficiency of the main results.     

An Algorithm for the Computation of the Transfer Function Matrix of Two-dimensional Systems

An algorithm is developed for the computation of the transfer function matrix of a two-dimensional system, which is given in its state-space form, without inverting a polynomial matrix. A new transformation has been considered so that the well known Fadeeva's algorithm for regular systems can be used as the basis for the derivation of the present algorithm. The above transformation can be generally used in the reduction of many two-dimensional problems to the corresponding one-dimensional ones. The algorithm presented is well-suited for computer use.