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1.
In this paper, a new type generalized Lyapunov equation for discrete singular systems is proposed. Then it is applied to study problems such as pole clustering, controllability and observability for discrete singular systems. First, some necessary and sufficient conditions for pole clustering are derived via the solution of this new type Lyapunov equation. Further, the relationship between the solution of the Lyapunov equation and structure properties of discrete singular systems will be investigated based on these results. Finally, a type of generalized Riccati equation is proposed and its solution is used to design state feedback law for discrete singular systems such that all the finite poles of the closed-loop systems are clustered into a specified disk. 相似文献
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This paper discusses a generalized quadratic stabilization problem for a class of discrete‐time singular systems with time‐delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S‐procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete‐time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non‐singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples. 相似文献
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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. 相似文献
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We address the invertibility problem for switched systems, which is the problem of recovering the switching signal and the input uniquely given an output and an initial state. In the context of hybrid systems, this corresponds to recovering the discrete state and the input from partial measurements of the continuous state. In solving the invertibility problem, we introduce the concept of singular pairs for two systems. We give a necessary and sufficient condition for a switched system to be invertible, which says that the individual subsystems should be invertible and there should be no singular pairs. When the individual subsystems are invertible, we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs. Detailed examples are included. 相似文献
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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. 相似文献
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The problem of static output feedback control is investigated for discrete singular systems with Markovian jump. Two necessary and sufficient conditions for the discrete singular Markovian jump system to be regular, causal and stochastically stable are proposed in terms of linear matrix inequality (LMI) approach. Two kinds of design methods of the desired mode‐independent static output feedback controller are given. The explicit expressions for the desired controller are also given. Numerical examples are proposed to show the validness of the developed results. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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This paper is concerned with the problem of reachable set estimation for discrete‐time singular systems with bounded input disturbances. Based on the Lyapunov method, a new sufficient condition is established in terms of linear matrix inequality (LMI) to guarantee that the reachable set of discrete‐time singular system is bounded by the intersection of ellipsoids. Then the result is extended to the problem for discrete‐time singular systems with time‐varying delay by utilizing the delay‐dependent approach and free weighting matrices. Two numerical examples are provided to demonstrate the effectiveness of the obtained results proposed in this paper. 相似文献
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离散广义区间动力系统的稳定性 总被引:1,自引:0,他引:1
利用范数理论,研究离散广义区间动力系统的稳定性问题,给出其区间动力系统的正则、因果且稳定的充分条件.在此基础上,进一步考虑该系统的区间极点集的配置问题,给出了使离散广义区间动力系统的极点落在预先给定园盘内的判定定理.数值算例表明了该方法的可行性. 相似文献
10.
Xin-Zhuang Dong 《International journal of systems science》2013,44(12):2101-2110
This paper investigates the problem of state feedback robust admissible control for singular delta operator systems with norm-bounded coefficient matrix uncertainties. A necessary and sufficient condition is derived to ensure the admissibility of the closed-loop singular delta operator system for all allowable uncertainties. Then, by specifying the structure of some matrix variables, the existence condition and explicit expression of a robust admissible controller are obtained in terms of strict linear matrix inequalities. Moreover, from the relation between singular discrete systems and singular delta operator systems, the corresponding results are also presented for uncertain singular discrete systems. Finally, some numerical examples are provided to demonstrate the effectiveness of the results in this paper. 相似文献
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Xin-zhuang Dong Mingqing Xiao 《International Journal of Control, Automation and Systems》2015,13(3):643-651
This paper studies the problem of state feedback H ∞ control for singular systems through delta operator approach. A necessary and sufficient condition is presented such that a singular delta operator system is admissible with a prescribed H ∞ performance, which can provide a unified framework of the existing H ∞ performance analysis results for both continuous case and discrete case. The existence condition and explicit expression of a desirable H ∞ controller are also obtained for singular delta operator systems. The proposed design method can be used for both singular continuous systems and singular discrete systems directly. The corresponding design procedures, which simplify the classical approaches, are discussed and presented. All obtained conditions in this paper are in the form of strict linear matrix inequalities whose feasible solutions can be found by standard linear programming method. Numerical examples are provided to illustrate the effectiveness of the theoretical results obtained in this paper. 相似文献
12.
Shengyuan Xu Chengwu Yang 《Automatic Control, IEEE Transactions on》2000,45(7):1405-1409
Deals with the problem of state feedback H∞ control for discrete singular systems. It is not assumed that the singular system under consideration is necessarily regular. The problem we address is the design of a state feedback controller, such that the resulting closed-loop system is not only regular, causal, and stable, but also satisfies a prescribed H∞-norm-bound condition. In terms of certain matrix inequalities, a necessary and sufficient condition for the solution to this problem is obtained, and a suitable state feedback-control law is also given 相似文献
13.
This paper investigates the problem of exponential stability and l1‐gain performance analysis for a class of discrete‐time switched positive singular systems with time‐varying delay. Firstly, a necessary and sufficient condition of positivity for the system is established by using the singular value decomposition method. Then by constructing an appropriate co‐positive Lyapunov functional and using the average dwell time scheme, we develop a sufficient delay‐dependent condition and identify a class of switching signals for the switched positive singular system to be exponentially stable and meet a prescribed l1‐gain performance level under the switching signal. Based on this condition, the decay rate of the system can be tuned and the optimal system performance level can be determined by solving a convex optimization problem. All of the criteria obtained in this paper are presented in terms of linear programming, which suggests a good scalability and applicability to high dimensional systems. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
14.
研究了不确定离散奇异系统的鲁棒H∞控制问题, 控制目标是设计一个状态反馈控制器, 对所有允许的不确定性, 闭环系统正则、因果、稳定且具干扰衰减度γ. 首次提出了该问题的充分必要条件, 并且设计方法归结为求一个严格线性矩阵不等式(LMI)的可行性问题. 最后, 通过一个数值实例证实了该方法的有效性. 相似文献
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Consensus problems are studied for both continuous‐time and discrete‐time multi‐agent singular systems with time‐invariant and directed communication topologies. Under restricted system equivalence of singular agents, sufficient and necessary conditions are obtained for admissible consensus ability with static protocols, which are based on both the relative information of the dynamic states and the absolute information of the static states. For a network of continuous‐time singular systems, the existence of admissible consensualization can be cast into strong stabilizability of the agent dynamics. Once discrete‐time multi‐agent singular systems satisfy the condition of reaching nontrivial final consensus states, strong stabilizability is a sufficient condition to achieve admissible consensualization. Two algorithms are proposed to construct two protocols, which are based on a linear matrix inequality and a modified Riccati equation, respectively. Finally, the algorithms are illustrated by two simulation examples. 相似文献
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《International journal of systems science》2012,43(15):2824-2837
ABSTRACTIn this paper, the problem of finite-time stability and stabilisation for positive singular discrete-time linear systems with time-varying delay is investigated. We first present novel delay-dependent sufficient conditions for positivity and finite-time stability of the unforced systems. We then apply the obtained results to solve finite-time stabilisation problem of the considered systems. The sufficient conditions for the positivity and finite-time stabilisable of such systems are formulated in terms of a standard linear programming (LP) problem. Numerical examples are provided to illustrate the effectiveness and advantages of our results. 相似文献
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A probabilistic discrete event system (PDES) is a nondeterministic discrete event system where the probabilities of nondeterministic transitions are specified. State estimation problems of PDES are more difficult than those of non-probabilistic discrete event systems. In our previous papers, we investigated state estimation problems for non-probabilistic discrete event systems. We defined four types of detectabilities and derived necessary and sufficient conditions for checking these detectabilities. In this paper, we extend our study to state estimation problems for PDES by considering the probabilities. The first step in our approach is to convert a given PDES into a nondeterministic discrete event system and find sufficient conditions for checking probabilistic detectabilities. Next, to find necessary and sufficient conditions for checking probabilistic detectabilities, we investigate the “convergence” of event sequences in PDES. An event sequence is convergent if along this sequence, it is more and more certain that the system is in a particular state. We derive conditions for convergence and hence for detectabilities. We focus on systems with complete event observation and no state observation. For better presentation, the theoretical development is illustrated by a simplified example of nephritis diagnosis. 相似文献
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