Duality of 2-D singular systems of Roesser models

In this paper, the properties and concepts of dual systems of the two-dimensional singular Roesser models （2-D SRM） are studied. Two different concepts of the dual systems are proposed for the 2-D SRM. One is derived from the duality defined for two-dimensional singular general models （2-D SGM）-called the S-dual systems; the other one is defined based on 2-D SRM in a traditional sense-called the T-dual systems. It is shown that if a 2-D SRM is jump-mode free or jump-mode reachable, then it can be equivalently transformed into a canonical form of a 2-D SRM, for which the T-duality and the S-duality are equivalent. This will be of some perspective applications in the robust control of 2-D SRM.     

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.     

基于观测器的2-D奇异系统Roesser模型的H∞滤波

This paper discusses the problem of the H∞ filtering for discrete time 2-D singular Roesser models (2-D SRM). The purpose is to design an observer-based 2-D singular filter such that the error system is acceptable, jump modes free and stable, and satisfies a pre-specified H∞ performance level. By general Riccati inequality and bilinear matrix inequalities (BMI), a sufficient condition for the solvability of the observer-based H∞ filtering problem for 2-D SRM is given. A numerical example is provided to demonstrate the applicability of the proposed approach. Key words 2-D singular systems, jump modes, general Riccati inequality, bilinear matrix i     

2-D奇异系统Roesser模型的鲁棒H∞控制

考虑具有参数不确定性的2-D奇异系统Roesser模型(简称2-D SRM)鲁棒H∞控制问题．在给出界实引理的另一等价形式的基础上,通过求解矩阵不等式,给出了不确定2-D奇异系统鲁棒H∞控制问题可解的充分条件及静态状态反馈控制律设计的代数表达式．最后通过一个仿真算例验证了方法的有效性．     

Bounded real lemma and robust control of 2-D singular Roesser models

This paper discusses the problem of robust H_∞ control for linear discrete time two-dimensional (2-D) singular Roesser models (2-D SRM) with time-invariant norm-bounded parameter uncertainties. The purpose is the design of static output feedback controllers such that the resulting closed-loop system is acceptable, jump modes free, stable and satisfies a prescribed H_∞ performance level for all admissible uncertainties. A version of bounded realness of 2-D SRM is established in terms of linear matrix inequalities. Based on this, a sufficient condition for the solvability of the robust H_∞ control problem is solved, and a desired output feedback controller can be constructed by solving a set of matrix inequalities. A numerical example is provided to demonstrate the applicability of the proposed approach.     

不确定2-D 奇异系统Roesser 模型 鲁棒能稳的矩阵不等式方法

考虑具有参数不确定性的2-D奇异系统Roesser模型(简称2-D SRM)鲁棒能稳问题．通过静态状态反馈控制律，使得对所有容许的不确定参数，闭环系统容许、稳定、无跳跃模．通过求解矩阵不等式，给出了不确定2-D奇异系统鲁棒能稳问题可解的充分条件及静态状态反馈控制律设计的代数表达式．最后通过算例验证了方法的有效性．     

H ∞ control for 2-D singular delayed systems

This article considers the problem of H _∞ control for two-dimensional (2-D) singular delayed systems in Roesser models. The problem to be addressed is the design of a state feedback controller such that the acceptability, internal stability and causality of the resulting closed-loop system is guaranteed and a prescribed H _∞ performance level is ensured. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the problem is obtained. A desired state feedback controller can be designed by solving a certain LMI. A numerical example is provided to demonstrate the application of the proposed method.     

Analysis and control of the jump modes behavior of 2-D singular systems—Part II: Regular observer and compensator design

This paper considers the problems of regular observer and compensator design for 2-D acceptable singular systems. First, the notions of jump mode reconstructability and jump mode reachability for 2-D acceptable singular systems are proposed. Necessary and sufficient conditions are presented for the jump mode reconstructability and reachability, respectively. Then, we show that there exists a reduced order regular observer for a 2-D acceptable singular system if the system is detectable and jump mode reconstructable, while there exists a reduced order regular compensator for a 2-D acceptable singular system if the system is stabilizable and jump mode reachable.     

二维广义系统的实现方法

给出两种二维广义系统的实现方法，第一种方法是通过两次一维广义实现来完成一种特殊的广义Ｒｏｅｓｓｅｒ模型实现；第二种方法根据两个二维广义系统实现与它们的传递函数阵乘积的实现关系，把待实现的二维传函函数阵与写成容易实现的传递函数矩阵乘积的形式而得到原系统的实现。     

离散奇异摄动系统稳定性分析

讨论了关于离散奇异摄动系统的摄动稳定性解析条件, 给出了离散奇异摄动系统两种模型下的摄动稳定性充要条件. 通过分析状态矩阵的结构特性, 得出了系统稳定所需要的状态矩阵形式和限制条件. 同时, 通过广义系统途径也得到了 2-D 离散奇异摄动 Roessor 模型稳定的充分条件.     

Regular unknown input functional observers for 2-D singular systems

This paper concerns with asymptotic regular unknown input functional observers (UIFOs) for two-dimensional (2-D) acceptable singular systems described by the Fornasini-Marchesini local state-space second model. A sufficient condition for the existence of an asymptotic regular UIFO is first presented in terms of a rank condition on the given system matrices. Based on this, an asymptotic 2-D regular UIFO is constructed using a linear matrix inequality (LMI) technique, while a new method is also given for designing regular functional observers for 2-D acceptable singular systems. Two illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed method.     

2-D奇异系统的实现

讨论了２－Ｄ奇异线性常系数一般模型（２－ＤＳＧＭ）在标准边界条件下的状态空间实现问题,提出了一种新的实现算法。     

2-D 奇异系统的实现

讨论了２－Ｄ奇异线性常系数一般模型（２－ＤＳＧＭ）在标准边界条件下的状态空间实现问题,提出了一种新的实现算法。     

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     

Stabilization of singular 2-D continuous-discrete systems bystate-feedback controllers

Necessary and sufficient conditions are established for the existence of a solution to the stabilization problem for singular two-dimensional (2-D) continuous-discrete linear systems. A procedure is presented for designing a state-feedback controller such that the closed-loop system is asymptotically stable, and its response is impulse-free     

Perfect observers for singular 2-D Fornasini-Marchesini models

A concept of the perfect observer for singular two-dimensional (2-D) Fornasini-Marchesini models is proposed. Sufficient conditions are established for the existence of the perfect observer. A procedure for design of the perfect observer is also derived and illustrated by a numerical example     

General response formula and minimum energy control for the generalsingular model of 2-D systems

The general response formula for the general singular model of 2-D linear systems is derived. The concepts of local reachability and local controllability are extended to the singular model. Necessary and sufficient conditions for local reachability and local controllability are established. The minimum energy control problem for the singular model is formulated and solved     

Stability analysis for 2-D switched Takagi-Sugeno fuzzy systems with stable and unstable subsystems

This paper is concerned with the problem of stability of two-dimensional (2-D) switched Takagi-Sugeno (T-S) fuzzy systems with stable and unstable subsystems described by the Roesser model with constant delays. The T-S fuzzy model is applied to close the discrete-time nonlinear subsystems. By utilizing the definitions of mode-dependent average dwell time (MDADT) method and a quasi-alternative switching signal, the stability condition for 2-D discrete-time switched systems composed of stable and unstable subsystems is derived, and a study on one-dimentional (1-D) system can be seen as a special case. Finally, the effectiveness and advantage of the obtained results are illustrated through practical example by LMI toolbox.     

The singular general model of 2D systems and its solution

A general singular model for 2D linear discrete systems with constant coefficients is defined. Necessary and sufficient conditions for the existence of a solution to the model are established. The considerations of the author's previous work (1986) can be extended to singular models of 2D linear systems with variable coefficients     

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。