线性时滞系统时滞独立稳定的充分条件

利用Lyapunov稳定性理论，通过一个推广的Lyapunov矩阵方程得出时滞独立稳定的充分条件，基于这个充分条件建立了几个判定线性时滞系统稳定性的简单判据，并推导出系统具有任意指定收敛速度指数稳定的充分条件。计算例子说明了所得结果的有效性。     

不确定变时滞线性系统的镇定条件

研究含时变非结构不确定性的变时滞线性系统的镇定控制器设计问题，基于代数Riccati方程的处理方法，提出了使其闭环系统渐近稳定的无记忆反馈控制器的设计方案．此外，还导出了两组直接由系统参数表示的鲁棒镇定条件．文末给出了用以阐明所得结果的数值算例，并与已有的结果进行了比较．     

Sufficient Conditions for Stability of Periodic Linear Impulsive Delay Systems

For a linear periodic system with impulsive action and delay, new approaches to the study of stability were proposed on the basis of the methods of spectral theory of linear operators, direct Lyapunov method, and N.G. Chetaev method for construction of the Lyapunov functions for the periodic linear systems, as well as the perturbation method for construction of the Lyapunov functions. These methods underlie the sufficient conditions for asymptotic stability of the linear periodic systems with impulsive action and delay. We gave some illustrative examples of studying stability of such systems under different assumptions about the dynamic properties of the continuous and discrete components of the impulsive system.     

Necessary and Sufficient Conditions for the Passivicability of Linear Distributed Systems

For a wide class of systems, as is known, hyper-minimal phase is necessary and sufficient for the strict passivicability of a system. This class contains both concentrated- and distributed-parameter systems, including parabolic equations that describe heat-exchange and diffusion processes. Our results are applicable to finite-dimensional input and output spaces, which are important for application and cover systems with different numbers of inputs and outputs for which passivity is superseded by the G-passivity of some rectangular matrix G. An example of a diffusion-type one-dimensional partial differential equation directly containing control is given. Proofs are based on the infinite-dimensional variant of the Yakubovich–Kalman lemma and Nefedov–Sholokhovich exponential stabilization theorem.     

Set Invariance Conditions for Singular Linear Systems Subject to Actuator Saturation

In this note, we establish a set of conditions under which an ellipsoid is contractively invariant with respect to a singular linear system under a saturated linear feedback. These conditions can be expressed in terms of linear matrix inequalities, and the largest contractively invariant ellipsoid can be determined by solving an optimization problem with LMI constraints. With the feedback gain viewed as an additional variable, this optimization problem can be readily adapted for the design of feedback gain that results in the largest contractively invariant ellipsoid. Moreover, in the degenerate case where the singular linear system reduces to a regular system, our set invariance conditions reduce to the existing set invariance conditions for normal linear systems.     

具有时变时滞的线性大系统的稳定条件

通过对系统微分方程解的估计,讨论一类具有时变时滞的线性大系统的稳定性,所导出的稳定性判别条件包括系统与时滞无关和与时滞相关稳定的充分条件,然后讨论了大系统的鲁棒稳定条件,并与相关文献进行比较,计算实例表明,所得出的结果改进了现有文献的研究结果。     

Mesh of Linear Arrays for Template Matching

This paper presents the architecture and the implementation of template matching on a 3-D piece-wise regular processor space that forms a two-dimensional array of linear systolic arrays. Template matching can be considered as a 2-D convolution of an image of sizeN × Nwith a kernel of sizer× r. Conventional high-speed implementations use 2-D systolic arrays of sizeO(r²) which compute inO(N²) time. The drawback of this solution is that the size of the processor array follows on the size of the convolution kernel. This does not permit the allocation of more processors in order to meet the real-time requirements. With the approach used in this paper, the size of the processor array may be extended up toO(sr²), 1 ≤s≤N, thereby accomplishing the calculations inO(N²/s) time. In the case whens=r, ther × rmesh of 1-D systolic arrays of sizeO(r) is yielded. The piecewise regularity of the 3-D processor array allows also easy physical realization.     

二阶线性切换系统指数镇定的充要条件

考虑二阶切换系统的镇定问题. 基于极坐标表示, 揭示了由锥形区域所界定的切换控制与子系统几何性质之间的自然联系. 由此, 建立了可镇定的充分必要条件; 并从代数与几何两方面刻画了镇定切换控制的特征. 进而给出了状态轨线指数收敛率的估计, 并阐释了由切换产生极限环与滑模运动的机理. 数值例子详细说明了结论的有效性.     

Algebraic Necessary and Sufficient Conditions for the Controllability of Conewise Linear Systems

The problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable. This paper focuses on conewise linear systems, i.e., systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions. For this class of systems, we present algebraic necessary and sufficient conditions for controllability. We also show that the classical results of controllability of linear systems and input-constrained linear systems can be recovered from our main result. Our treatment employs tools both from geometric control theory and mathematical programming.     

Relaxed Conditions for the Exponential Stability of a Class of Linear Time-Varying Systems

This technical note states new sufficient conditions for the exponential stability of linear time-varying (LTV) systems of the form $mathdot{x}(cdot)=A(t)x(t)$. The approach proposed derives and uses the notion of perturbed frozen time (PFT) form that can be associated to any LTV system. Exploiting the Bellman-Gronwall lemma, relaxed stability conditions are then stated in terms of “average” parameter variations. Salient features of the approach are: pointwise stability of $A(cdot)$ is not required, $Vertmathdot{A}(cdot)Vert$ may not be bounded, the stability conditions also apply to uncertain systems. The approach is illustrated by numerical examples.      

Robust Stability Conditions for a Family of Linear Discrete-Time Systems Subjected to Uncertainties

Automation and Remote Control - Robust stability conditions are established for a family of linear discrete-time systems subjected to uncertainties. The traditional approach, which involves the...     

离散混沌系统的线性和非线性反馈同步法及其条件

基于离散系统稳定性理论和Pecora-Carroll混沌同步定理，研究了多变量离散混沌系统的同步问题．提出了线性和非线性反馈同步控制方法，同步系统反馈控制器由线性和非线性两部分组成，响应系统受驱动系统的所有变量驱动．通过分析误差系统的特征方程和计算响应系统的最大条件Lyapunov指数，分别导出了离散混沌系统的同步条件．将该方法应用于Henon映射系统，实现了两Henon混沌系统的同步控制．讨论了混沌系统的同步性能与控制参数的关系．基于Matlab软件的数值仿真结果表明了该方法的有效性．     

Pipelined Diagnosis of Wafer-Scale Linear Arrays

We present a comparison-based algorithm for identifying faulty and fault-free elements in a wafer-scale linear array of processors (or other logic elements). Only nearest neighbor communication is assumed to be possible between the processors in the array. Because the algorithm is simple and requires no storage of test vectors or test outcomes, it is ideally suited for implementation on the wafer to provide the capability for built-in production (or post production) testing. We show that, surprisingly, this method achieves high accuracy of diagnosis over a wide range of yields even though the diagnosis may be based on a high proportion of results produced by faulty processors. We also propose an improvement to the above algorithm which uses a processor diagnosed as fault-free by the basic algorithm as the starting point in improving the accuracy with which faulty processors are identified. Quantitative and qualitative reasoning validate the efficiency of these schemes.     

Efficient Deterministic and Probabilistic Simulations of PRAMs on Linear Arrays with Reconfigurable Pipelined Bus Systems

In this paper, we present deterministic and probabilistic methods for simulating PRAM computations on linear arrays with reconfigurable pipelined bus systems (LARPBS). The following results are established in this paper. (1) Each step of a p-processor PRAM with m=O(p) shared memory cells can be simulated by a p-processors LARPBS in O(log p) time, where the constant in the big-O notation is small. (2) Each step of a p-processor PRAM with m=(p) shared memory cells can be simulated by a p-processors LARPBS in O(log m) time. (3) Each step of a p-processor PRAM can be simulated by a p-processor LARPBS in O(log p) time with probability larger than 1–1/p^c for all c>0. (4) As an interesting byproduct, we show that a p-processor LARPBS can sort p items in O(log p) time, with a small constant hidden in the big-O notation. Our results indicate that an LARPBS can simulate a PRAM very efficiently.     

Embedding of Systems. Conditions of the Strict Insensitivity of Linear Systems to Nonextensive Structural Disturbances

Conditions are considered of the invariance of linear stationary dynamic systems, the quality of operation of which is described by an aggregate of matrix transfer functions, to structural disturbances representable in the operator form of the notation of a mathematical model without changes in the dimensions of matrices entering into this model. Parametric disturbances represent mearly a composite portion of the disturbances under examination. On the basis of the use of the technology of embedding of systems, the necessary conditions of existence of the invariance to the disturbances under study are found and also complete sets of the disturbances that do not affect the quality of operation of a system are described. An illustrative example is given.     

Model Checking Linear Programs with Arrays

In previous work we proposed Linear Programs as a fine grained model for imperative programs, and showed how the model checking procedure used in SLAM can be generalised to a model checking procedure for Linear Programs. In this paper we show that our model checking procedure for linear programs can be extended in such a way to support the analysis of linear programs featuring a symbol for undefined values and conditional expressions. This extension is particularly important as it paves the way to the construction of model checking procedures for wider classes of imperative programs such as, e.g., linear programs with arrays. We provide a detailed account of a symbolic model checking procedure for this extended class of linear programs, discuss its implementation in the eureka tool, and present experimental results that confirm its effectiveness in the analysis of linear programs with arrays.     

Circular Criteria for Linear Systems

Circular stability and unstability criteria for linear time-varying systems are formulated. They are applicable to verify the stability of linear systems for which the matrix in the right side have eigenvalues with positive real parts at certain specific time instants.     

线性系统的鲁棒D稳定性分析

1　引言近年来 ,结合系统过渡过程特性的考虑 ,对系统极点在某一特定区域 D中的系统 D稳定性的鲁棒特性分析问题已为众多学者所研究 [1～ 4] .对具有结构和非结构摄动的线性系统 ,导出了保持系统 D稳定性的允许摄动范围 .文献 [1 ,2 ]考虑了一些特定的区域 ,而文献[3,4]则采用 Gutman和 Jury[5] 提出的根束理论 ,对一类更一般的区域 ,导出了其鲁棒 D稳定性条件 .这些研究所采用的方法就是基于 D稳定性准则 ,给出关于摄动界的关系式 ,所得到的关系式一般都依赖一些参数 .通过适当选取这些参数 ,得到允许摄动界 .但是 ,这些参数和允许摄动…     

一类不确定线性系统的鲁棒线性控制器设计

针对一类不确定性不满足匹配条件的线性系统,利用Lyapunov方程和不确定项的范数界,分别设计了具有可调参数和鲁棒线性状态和输出控制器。这些可调参数可以依据不确定项的范数界的大小来选取,具有一定的灵活性。