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.     

Distributed control of time-delay interconnected nonlinear systems

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators.     

Model-based event-triggered control of switched discrete-time systems

In this paper, we aim to study model-based event-triggered control for a class of uncertain switched discrete-time systems composed of stabilizable and unstabilizable subsystems. A nominal model is introduced at the controller side to form a dynamic controller so that it can provide a kind of approximate estimate of the system state for system input even the overall switched discrete-time system is running in open-loop during any two consecutive event-triggered instants. By using multi-Lyapunov function method and the average dwell time switching strategy, stability conditions given in linear matrix inequality form for the closed-loop switched discrete-time system are derived. The design of control gains is also given. Finally, a numerical example and a physical example are provided to verify the effectiveness and usefulness of the proposed method.     

Controller design via the synthesis equation

A comprehensive and efficient frequency domain methodology for the design of controllers for high order single-input-single-output (SISO) plants is presented. The unique advantage of the methodology is that it enables the designer to readily visualize the optimum structure for the controller in the early stage of design. This eliminates time consuming and often frustrating trial-and-error iterations in controller design which is characteristic of many of the current methods. The methodology has been motivated by the need for a streamlined procedure to directly synthesize a low order, robust controller with which the controlled step response can be made to closely match that of a prespecified reference model. The method does not require order reduction of the original model. Also, only output feedback is utilized. The method is applicable to non-minimum phase, unstable, and irrational plant transfer functions. It is ideally suited to design local controllers for the subsystems so that they replicate low order models with compatible dynamic characteristics. Examples are given to demonstrate the method.     

Analysis of Repeated Systems with Non- identical,Non-commutative Interactions Using Bond Graph Adapted Operator Perturbation

A technique is presented to study the dynamics of a class of repeated systems with non-commutative interactions. The system equations are formulated using tensor product algebra. A pre-analysis of the system equations is carried out to reduce the interactions to a small perturbing operator. The formal operator perturbation scheme is discussed. The procedure of pretreatment is adapted to bond graph techniques for the ease of representation of dynamic systems. It is shown that the method of operator perturbation may also be handled very conveniently by bond graph approach. The overall system dynamics can be studied from the analysis of the subsystems coupled through the perturbing operator. This results in a substantial reduction in the size of the problem to be considered. The procedure is illustrated by suitable examples.     

线性流形上次反对称矩阵的次特征值的反问题

讨论了线性流形上次反对称矩阵的次特征值的反问题,给出了解存在的条件,并给出了解的通式。本文充分利用了次单位矩阵的作用,将次反对称矩阵的次特征值的反问题转为反对称矩阵的逆特征值问题来解决。     

Applications of clustering to information system design

Given the difficulty of designing and creating information systems of many components and interconnections, it is commonplace to find these tasks accomplished by means of a partition into subsystems. Later the distinct subsystems are made to interface with one another and an overall system is achieved. The purpose of the present paper is to point out the availability of methods for effecting the partition in optimal or approximately optimal ways. Clustering algorithms for the specific case of information systems are obtained and exemplified.     

中国技术转移体系的演化状态及协同机制研究

本文以回顾我国技术转移体系的演进历程为逻辑起点,对技术转移体系的内容、特征及机制进行阐述,从纵向视角对我国技术转移体系进行解析,将其分为五个子系统,运用复合系统协同度模型对我国技术转移体系的内部演化状态进行测度。研究发现:我国技术转移体系呈现良好的演化态势,但总体水平较低,其薄弱环节为技术中介和扩散系统,表明仅强调某个系统的发展而忽视其它子系统,难以实现技术转移体系的协同发展。最后,尝试性地构建我国技术转移协同运行机制,以供我国技术转移实践之参考。     

关于伴随矩阵性质的进一步讨论

进一步讨论了伴随矩阵的秩、可逆性、特征值及一些特殊矩阵的伴随矩阵,并加以证明,力争对伴随矩阵有一个较完整的认识。     

Stabilization of switched linear singular systems with state reset

This paper investigates the stability and stabilization of switched linear singular systems with state reset at switching instants. Based on the dynamics decomposition of singular subsystems, a sufficient stability condition for the system with the given state reset is obtained. Then, the stabilization problem by state reset is investigated and an algorithm for computing the reset matrices is presented. The obtained results extend some previous works on both singular switched systems and reset control for normal switched systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.     

Quadratic stability analysis and robust distributed controllers design for uncertain spatially interconnected systems

This paper is concerned with the quadratic stability analysis and robust distributed controllers design of both continuous-time and discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). The well-posedness, quadratic stability, and contractiveness of USISs are properly defined for the first time. A sufficient condition employing the given system matrices is established to check the well-posedness, quadratic stability and contractiveness. This condition is simpler than the existing conditions based on the decomposition of system matrices. Based on the new condition derived, a sufficient condition is given for the existence of robust distributed controllers and a constructive method is then presented for the design of robust distributed controllers. The advantage of the proposed constructive approach is that it employs the given system matrices while the existing methods conduct the bilinear transformation on these matrices when design controllers, and consequently, the constructive approach in this paper is computationally more efficient than the existing methods. Several examples are included to demonstrate the simplicity, efficiency and applicability of the derived theoretical results.     

Model reduction using the stability-equation method and the Padé approximation method

A combined method making use of the advantages of the stability-equation method and the Padé approximation method for reducing high order transfer functions of single-input/single-output systems and multivariable systems is presented. The reduction procedure is simple and computer-oriented. All the reduced models are guaranteed to be stable if the original system is stable. The proposed method is applied to the investigation of (1) the effect of model reduction on the limit-cycle of non-linear systems and (2) the effect of model reduction on Horowitz compensators. Detailed calculations are given and comparisons with results in the current literature are made.     

Non-weighted H∞ performance for 2-D FMLSS switched system with maximum and minimum dwell time

This paper investigates the H_∞ performance of two-dimensional (2-D) switched system represented by Fornasini–Marchesini local state-space (FMLSS) model with maximum and minimum dwell time approach. By using the multiple Lyapunov function approach, and designing a set of switching signals subject to maximum and minimum dwell time characteristic, respectively, for all stable subsystems or both stable and unstable subsystems exist, we give the sufficient condition on exponential stability of the given switched system, and propose the sufficient condition which can guarantee that the given switched system is exponentially stable and has a specified H_∞ disturbance attenuation level γ. All the results obtained are on normal noise attenuation index of strictly non-weighted form, which are better than the existing results on weak one of weighted form from the physical point of view. Finally, numerical examples are presented to display the effectiveness of the proposed results.     

Realization and canonical representation of linear systems through I/O maps

In this paper, we use input and output maps to develop simple procedures to obtain minimal realizations for linear continuous-time systems. The procedures developed are numerically efficient and yield explicit formulae for the state-space matrices of the realization in terms of the system parameters, notably the system eigenvalues. Both systems with distinct eigenvalues and repeated eigenvalues are treated. We also present a procedure for transforming a realization obtained through the input or output map to Jordan canonical form. The transformation matrices required to transform the realization to Jordan canonical form are specified entirely in terms of the system eigenvalues. We illustrate the results obtained with several examples.     

Incremental H∞ performance for a class of stochastic switched nonlinear systems

In this paper, we investigate the incremental H_∞ performance problem for a class of stochastic switched nonlinear systems by using a state-dependent switching law and the maximum and minimum dwell time approach. By resorting to the state-dependent switching law, some sufficient conditions are provided to cope with the incremental H_∞ performance problem, which can be applied even if all subsystems are unstable. Then, based on the maximum and minimum dwell time scheme, the incremental H_∞ performance problem to be solvable is derived for two cases: one is all subsystems are incrementally globally asymptotically stable in the mean(IGASiM), another is both IGASiM subsystems and unstable subsystems coexist. When all subsystems are IGASiM, the stochastic switched nonlinear system is IGASiM and possesses a incremental L₂-gain under given conditions. When both IGASiM subsystems and unstable subsystems coexist, if the activation time ratio between IGASiM subsystems and unstable ones is not less than a specified constant, the sufficient conditions for the incremental H_∞ performance of the stochastic switched nonlinear system are given. Two numerical examples are given to illustrate the validity of methods proposed.     

Time-domain simplification of linear time-invariant systems using cauer continued-fraction expansion about sa and s0 alternately

A simple time-domain procedure is presented for deriving simplified models for linear time-invariant systems. It is based on deriving a new realization form for the Cauer continued fraction expansion about s  a and s  0 alternately. A new similarity transformation is also developed which can be used to construct approximate aggregation matrices for the reduced order models obtained by the proposed procedure. Particularly when the original state-space model is in a phase-variable canonical form, the similarity matrix is given explicitly.     

大连市气候变化适应度评价

选取大连市1960年-2009年月平均气温和降水量资料,运用线性倾向估计和Morlet小波分析探讨了近50a大连市气候变化特征,表明50a来年均气温显著上升,其中冬、春季的增幅最大,降水量总体上呈下降趋势,基本经历了＂减少-增加-减少-增加＂的变化过程。在此背景下,根据系统之间的动态耦合原理,选取社会、经济、农业和资源环境系统作为大连市气候变化适应度的评价子系统,利用主成分分析法,确定2000年-2009年气候系统与评价系统的综合发展水平,然后运用模糊数学中的隶属度函数,判定大连气候变化的适应度。结果表明：2000年-2009年大连市气候系统的综合发展水平波动性较大,但总体上处于上升态势,评价子系统的发展水平也显著提高,而且两者具有明显的阶段性特征;2000年-2009年大连市气候变化的适应度总体上呈微弱的下降趋势,尤其是从2007年开始,下滑程度较大。     

基于耦合视角的流域初始水权配置框架初析——最严格水资源管理制度约束下

实行最严格水资源管理制度是解决我国日益复杂的水问题与实现水资源有效配置的崭新思路。明晰流域初始水权是落实最严格水资源管理制度的重要途径和技术支撑,流域初始水权配置的理论与实践必须适应这一制度的要求。面向最严格水资源管理制度的约束,本文结合国内外初始水权配置相关研究进展的系统梳理,在提出相关概念及剖析其内涵的基础上,以用水总量控制、用水效率控制和纳污量控制为基准,构建基于耦合视角的流域初始水权配置方法与理论框架,具体思路如下:1针对省区初始水权配置子系统,基于量质耦合获得流域内不同省区的初始水权量;2针对政府预留水量配给子系统,基于供需双侧耦合确定流域级政府预留水量;3为保障两个子系统协调发展,建立基于耦合协调性判别准则的循环耦合模型,获得流域初始水权配置推荐方案,并详细阐述该研究框架各组成部分的工作原理及其之间的工作关系。     

Decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems

This paper presents a novel approach to address the decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems. The overall system is composed of a number of discrete-time interconnected nonlinear subsystems at the presence of multiple faults occurring at unknown time-instants. In order to deal with the unknown interconnection effects and changes in model dynamics due to multiple faults, both passive and active fault tolerant control design are considered. In the Active fault tolerant case an online approximation algorithm is applied to estimate the unknown interconnection effects and changes in model dynamics due to multiple faults. Besides, the decentralized control strategy is implemented for each subsystem with the model predictive control algorithm subject to some constraints. It is showed that the proposed method guarantees input-to-state stability characterization for both local subsystems and the global system under some predetermined assumptions. The simulation results are exploited to illustrate the applicability of the proposed method.     

Model reduction for control systems with restricted complexity controllers

The problem of reduced-order modelling is considered in connection with the design of restricted complexity controllers. The suggested reduction method develops in two phases: (i) a simple frequency response of the overall feedback control system is determined according to the design specifications; (ii) a reduced-order transference of the controlled plant is obtained by solving a linear set of equations in such a way that its behaviour approximates that of the original plant at frequencies which are meaningful for the overall transfer function derived in the first step (e.g. resonance and cutoff frequencies). An example shows how the procedure yields a reduced-order model suitable for designing robust controllers whereas other standard methods, based on properties of the plant only, fail.