A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular model, called Forna- sini-Marchesini (FM) second model was proposed by Fornasini and Marchesini in 1978. The aim of this paper is to present a survey of the existing literature on the stability of FM second model.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

Stabilization of Discrete-time 2-D T-S Fuzzy Systems Based on New Relaxed Conditions

This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Delay-Dependent Robust H∞ Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

This paper considers the problem of delay-dependent robust optimal H∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent g-suboptimal state feedback robust H∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H∞ noise attenuation g over all admissible parameter uncertainties is established. Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H∞ controller which minimizes the H∞ noise attenuation g of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

Robust Optimal H∞ Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

子宫内膜癌患者血清NRP-2 VEGF-C和VEGF-D水平与其转移的相关性研究

目的 探究子宫内膜癌(EC)患者血清神经菌毛蛋白-2(NRP-2)、血管内皮生长因子C(VEGF-C)和血管内皮生长因子D(VEGF-D)水平与其转移的关系。方法 选取2020年5月至2024年2月华北理工大学附属医院收治的147例EC患者为研究对象,以病理结果为判定标准,根据癌细胞是否发生转移分为转移组(52例)和未转移组(95例),选取46例同期健康体检者为对照组,比较3组对象NRP-2、VEGF-C和VEGF-D水平,并分析与EC转移的关系。结果 转移组和未转移组的NRP-2、VEGF-C和VEGF-D水平均高于对照组,差异有统计学意义(P<0.05)。转移组的NRP-2、VEGF-C和VEGF-D水平均高于未转移组,差异有统计学意义(P<0.05)。转移组的内膜样癌占比、病理G1级占比和浸润深度≤1/2肌层占比均低于未转移组,差异有统计学意义(P<0.05)。非内膜样癌(OR=3.376,95%CI:1.037~10.995,P=0.043)、病理G2(OR=19.426,95%CI:2.895~130.338,P=0.002)或G3级(OR=11.311,95%CI:1.842~69.453,P=0.009)、浸润深度>1/2肌层(OR=10.683,95%CI:2.889~39.512,P<0.001)和高NRP-2水平(OR=1.847,95%CI:1.452~2.349,P<0.001)均是EC转移的独立危险因素。限制性立方样条分析结果显示,NRP-2与EC转移主要呈线性关系(P<0.001)。当NRP-2<17.35μg/L时,EC转移风险低;当NRP-2>17.35μg/L时,EC转移风险高。结论 子宫内膜癌患者血清NRP-2水平高与其转移有关,NRP-2水平升高是EC转移的独立预测因子。

H_∞ Control for 2-D Discrete State Delayed Systems in the Second FM Model

这份报纸涉及 H 控制的问题为二维(2-D ) 分离州的延期系统由第二 Fornasini 和 Marchesini (FM ) 描述了州空间当模特儿。为这个 2-D 系统有 H 噪音变细的一个足够的条件以某个线性矩阵不平等(LMI ) 被给。最佳的 H 控制器被解决一个凸的优化问题获得。最后，一个模拟例子被给说明建议结果的有效性。

Robust stability test for 2-D continuous-discrete systems with interval parameters

It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i. e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.

Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model

This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based sufficient condition for the existence of such controllers is established. Finally, a numerical example is provided to illustrate the applicability of the proposed method.

Novel l_2-l_∞ controller design for LPV discrete time-delay systems

One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present a parameter-dependent l 2-l ∞ performance criterion using a parameter-dependent Lyapunov function. Upon the conditions addressed, an improved parameter-dependent l 2-l ∞ performance criterion is established by the introduction of a slack variable, which exhibits a kind of decoupling between Lyapunov functions and system matrices. This kind of decoupling enables us to obtain more easily tractable conditions for analysis and synthesis problems. Then, the corresponding parameter-dependent state-feedback controller design is investigated upon these performance criteria, with sufficient conditions obtained for the existence of admissible controllers in terms of parameterized linear matrix inequalities. Finally, a numerical example is provided to illustrate the feasibility and advantage of the proposed controller design procedure.

Robust Non-Fragile Control of 2-D Discrete Uncertain Systems: An LMI Approach

This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

一种基于三角数分解的可配置2-D卷积器优化方法

多尺寸2-D卷积通过特征提取在检测、分类等计算机视觉任务中发挥着重要作用。然而,目前缺少一种高效的可配置2-D卷积器设计方法,这限制了卷积神经网络(CNN)模型在边缘端的部署和应用。该文基于乘法管理以及奇平方数的三角数分解方法,提出一种高性能、高适应性的卷积核尺寸可配置的2-D卷积器。所提2-D卷积器包含一定数量的处理单元(PE)以及相应的控制单元,前者负责运算任务,后者负责管理乘法运算的组合,二者结合以实现不同尺寸的卷积。具体地,首先根据应用场景确定一个奇数列表,列表中为2-D卷积器所支持的尺寸,并利用三角数分解得到对应的三角数列表;其次,根据三角数列表和计算需求,确定PE的总数量;最后,基于以小凑大的方法,确定PE的互连方式,完成电路设计。该可配置2-D卷积器通过Verilog硬件描述语言(HDL)设计实现,由Vivado 2 022.2在XCZU7EG板卡上进行仿真和分析。实验结果表明,相比同类方法,该文所提可配置2-D卷积器,乘法资源利用率得到显著提升,由20%~50%提升至89%,并以514个逻辑单元实现1 500 MB/s的吞吐率,具有广泛的适用性。

基于离散2-D小波多级分解的电容器外观缺陷视觉检测方法

电容器外观破损、凸起等缺陷直接影响器件的生产质量。目前电容器微小外观缺陷检测难度较大,导致视觉检测效率较低。为此提出了基于离散2-D小波多层分解的电容器外观缺陷视觉检测方法。采用同态滤波处理去除光照对电容器外观视觉检测结果的影响。利用像素点灰度值确定图像边缘点位置,提取电容器外观缺陷区域。应用离散2-D小波分解的方法对其展开多级分解。再差分统计电容器图像的外观缺陷纹理特征。将特征输入Mahalanobis分类器中,完成电容器外观缺陷视觉检测。仿真结果表明,所提方法可以较好检测电容的各种缺陷,召回率最低值是94.9%,误检率最高值为9.8%,漏检率均在10%以内,电容器缺陷检测效果较好。

A high-throughput VLSI design for JPEG2000 9/7 discrete wavelet transform

To achieve high parallel computation of discrete wavelet transform （DWT） in JPEG2000, a high-throughput two-dimensional （2D） 9/7 DWT very large scale integration （VLSI） design is proposed, in which the row processor is based on flipping structure. Due to the difference of the input data flow, the column processor is obtained by adding the input selector and data buffer to the row processor. Normalization steps in row and column DWT are combined to reduce the number of multipliers, and the rationality is verified. By rearranging the output of four-line row DWT with a multiplexer （MUX）, the amount of data processed by each column processor becomes half, and the four-input/four- output architecture is implemented. For an image with the size of N x N, the computing time of one-level 2D 9/7 DWT is 0.25N2 ＋ 1.5N clock cycles. The critical path delay is one multiplier delay, and only 5N internal memory is required. The results of post-route simulation on FPGA show that clock frequency reaches 136 MHz, and the throughput is 544 Msample/s, which satisfies the requirements of high-speed applications.

Discrete Element with Flexible Connector for Dynamic Analysis of 3-D Beam Structures

Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off-diagonal in a general case. The zero-length rigid element is introduced to simulate the node at which multiple elements are jointed together. It may also be effective when the axes of adjacent elements are not in the same line. The examples for eigenvalue calculation show that the model is successful. It can be extended to the geometric nonlinear response analysis.

Mixed Gl2／GH2 multi-channel multi-objective control synthesis for discrete time systems

This paper proposes a new approach for multi-objective robust control. The approach extends the standard generalized l2 (Gl2) and generalized H2 (GH2) conditions to a set of new linear matrix inequality (LMI) constraints based on a new stability condition. A technique for variable parameterization is introduced to the multi-objective control problem to preserve the linearity of the synthesis variables. Consequently, the multi-channel multi-objective mixed Gl2/GH2 control problem can be solved less conservatively using computationally tractable algorithms developed in the paper.

Event-triggered robust guaranteed cost control for two-dimensional nonlinear discrete-time systems

An event-triggered scheme is proposed to solve the problems of robust guaranteed cost control for a class of two-dimensional(2-D)discrete-time systems.Firstly,an eventtriggered scheme is proposed for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities.Then,according to the Lyapunov functional method,the sufficient conditions for the existence of event-triggered robust guaranteed cost controller for 2-D discrete-time systems with parameter uncertainties and sector nonlinearities are given.Furthermore,based on the sufficient conditions and the linear matrix inequality(LMI)technique,the problem of designing event-triggered robust guaranteed cost controller is transformed into a feasible solution problem of LMI.Finally,a numerical example is given to demonstrate that,under the proposed event-triggered robust guaranteed cost control,the closed-loop system is asymptotically stable and fewer communication resources are occupied.