对线性系统状态转移矩阵的讨论

状态转移矩阵是现代控制理论的重要概念,在线性控制系统的运动分析中起着重要的作用.分别对连续时间线性时变系统、离散时间线性定常系统以及离散时间线性时变系统的状态转移矩阵进行了研究.根据常微分方程和差分方程解的唯一性,得到了判断矩阵函数是某一线性系统状态转移矩阵的充分条件,并求出了其对应的系统矩阵.实践证明了结论的正确性.     

逆系统方法的径向基函数网络实现

研究采用径向基函数网络（ＲＢＦＮ）构造系统逆控制器的工程实现问题，同时给出该直接逆动态控制器存在的充分条件。为进一步改善基于ＲＢＦＮ的直接逆动态控制器的动态性能，对该伪逆系统进行ＰＩＤ综合。仿真研究表明，以ＲＢＦＮ拟合对象逆过程的ＰＩＤ综合控制策略不仅能改善系统的动态性能，而且具有良好的参数鲁棒性能。     

Improvement on Stability Analysis for Linear Systems Under State Saturation

This note considers the problem of stability analysis for linear systems under state saturation. With the introduction of set coverage that gives less constraint on the free matrix G , a less conservative sufficient global asymptotic stability condition is obtained and the corresponding iterative linear matrix inequality algorithm is given. A numerical example is given to show the effectiveness of the proposed method.     

Input-to-State Stabilization of Linear Systems With Quantized State Measurements

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in." Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time and analyzed with the help of a Lyapunov function, similarly to earlier work. The second strategy incorporates time sampling, and its analysis is novel in that it is completely trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work     

Reliable State Feedback Control Synthesis For Uncertain Linear Systems

This paper is concerned with the problem of designing reliable state‐ feedback control for a class of uncertain linear systems with norm bounded uncertainty. A procedure for designing reliable state‐feedback control is presented for the case of actuator faults that can be modeled by a scaling factor. In the design, the performance of the normal system (without fault) is optimized, as the considered system operates under the normal condition most of the time. In addition, when actuator faults occur, the closed‐loop system retains robust stability and satisfies a known quadratic performance bound. A numerical example is provided to illustrate the effectiveness of the proposed design method.     

矩阵求逆运算的VLSI实现

矩阵运算广泛应用于各类电路计算中,矩阵运算的硬件实现能够充分发挥硬件的速度和并行性.其中矩阵求逆是矩阵运算中重要的运算.为加速矩阵求逆,研究构造出一种非常易于实现的基于心动阵列的矩阵求逆的电路结构.通过硬件描述语言Verilog建模,VCS仿真及用Design Compile进行综合,结果表明这种并行结构能快速实现矩阵求逆,且运算精度较高.     

矩阵求逆运算的VLSI实现

矩阵运算广泛应用于各类电路计算中,矩阵运算的硬件实现能够充分发挥硬件的速度和并行性。其中矩阵求逆是矩阵运算中重要的运算。为加速矩阵求逆,研究构造出一种非常易于实现的基于心动阵列的矩阵求逆的电路结构。通过硬件描述语言Verilog建模,VCS仿真及用Design Compile进行综合,结果表明这种并行结构能快速实现矩阵求逆,且运算精度较高。     

一类线性移动计费系统的设计与实现

以某地区的移动计费系统为背景,采用软件工程为指导,将该地区的移动网连接在一起,并利用线性模型对系统进行了分析,同时给出了设计的方法。对移动计费系统的网络进行了分析,并给出了网络设计方案。提出了基于计费系统的线性模型,根据数学模型给出了移动计费系统软件的设计方法。通过现场实验证明,用户的通话效果良好、计费准确,有一定的推广性和科学价值。     

线性广义时滞系统的状态反馈H∞控制

首先利用线性矩阵不等式(LMI)方法,给出线性广义时滞系统稳定的一个充分条件;然后讨论广义时滞系统的H_∞状态反馈控制,给出控制器存在的充分条件,同时给出控制器的设计.控制器可由矩阵不等式解得。     

复杂串联系统的状态空间生成的形式化分析

大规模系统的模型状态空间生成过程由于状态空间的规模没有预先估计而不可控,形式化分析有利于解决这一问题。本文针对复杂串联系统的特殊结构,采用形式化方法分析研究了它的状态空间生成规律,从而达到快速预估模型状态空间规模的目的。     

State estimation for Markovian Jump Linear Systems with bounded disturbances

In this paper, we investigate the state estimation problem for a class of Markovian Jump Linear Systems (MJLSs) in the presence of bounded polyhedral disturbances. A set-membership estimation algorithm is first proposed to find the smallest consistent set of all possible states, which is shown to be expressed by a union of multiple polytopes. The posterior probabilities of the system jumping modes are then estimated by introducing the Lebesgue measure, based on which the optimal point estimate is further provided. Moreover, a similarity relationship for polytopes is defined and an approximate method is presented to calculate the Minkowski sum of polytopes, which can help reduce the computational complexity of the overall estimation algorithm.     

Robust Fault Detection for Switched Linear Systems With State Delays

This correspondence deals with the problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. The problem of robust fault detection is converted into an H _infin-filtering problem. By a switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

一类线性切换系统的鲁棒状态反馈镇定

考虑一类标称系统存在共同Lyapunov函数的切换系统的鲁棒镇定问题.在不确定性不满足匹配条件下,设计出鲁棒状态反馈控制器,并在给定的切换策略下,确保闭环系统在其平衡点处渐近稳定.仿真结果表明所设计控制器是有效的.     

Event-triggered Control of Positive Systems With State Saturation Using Linear Programming

This paper proposes the event-triggered control of positive systems with state saturation both in discrete-time and continuous-time cases. A 1-norm based event-triggered mechanism is established for positive systems. Under the event-triggered mechanism, the error term between actual and sample states is transformed into interval uncertain form. Together with the properties of saturation, the systems with state saturation are transformed into interval uncertain systems and the corresponding lower and upper bounds of the system matrices are obtained, respectively. Using a linear co-positive Lyapunov function, the event-triggered controller and the auxiliary gain matrix of the domain of attraction are designed in terms of linear programming, respectively. Then, the systems with state and input saturation are also described via interval uncertain systems. An event-triggered controller is designed and thus the closed-loop systems are positive and stable under the designed controller. Furthermore, the presented event-triggered control approach is extended to the continuous-time case. Compared to existing control approaches, the event-triggered control can reduce energy consumption and increase the practicability. Finally, several numerical examples are given to illustrate the effectiveness of the proposed design.

     

Delta域内线性系统的H2状态反馈控制

基于LMI方法研究了Delta算子描述下的线性定常系统的H2控制问题,利用Schur补性质推导出状态反馈控制律存在的充分必要条件,用一个线性矩阵不等式的可行解给出了状态反馈控制律的一个参数化表示。     

Controllability of Singularly Perturbed Linear Time-Dependent Systems with Small State Delay

A singularly perturbed linear time-dependent control system with multiple point and distributed small delays in state variables is considered. Two lower-dimension systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. The reduced-order and the boundary-layer systems are in separate time scales, and they do not contain the small parameter any more. Connections between the properties of controllability of these systems and such a property of the original system itself are established for all sufficiently small values of the parameter of singular perturbations.     

Ellipsoidal State Estimates of Linear Dynamic Systems: Their Limiting Behavior

In guaranteed estimation of the states of dynamic systems under deterministic bounded disturbances, use of made of outer ellipsoidal estimates that are optimal relative to the volume and sum of squares of the semiaxes of the ellipsoid. The boundedness and convergence of a sequence of such ellipsoids for stable discrete systems are investigated. The asymptotic behavior of these estimates mostly depends on the minimality criterion chosen for the ellipsoid dimension.     

On Asymptotic Stabilization of Linear Discrete-time Systems with Saturated State Feedback

As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.     

SISO线性系统的滑模变结构状态范数控制

在线性系统滑模控制理论的基础上,给出了对于一般SLSO线性系统状态范数控制的形式,提出了状态范数的控制器结构。基于李亚普诺夫稳定性理论证明了状态范数控制系统的闭环稳定性。然后分别针对状态范数控制器与趋近率控制和单位向量控制进行了数值仿真的分析与比较,结果说明状态范数控制综合了趋近率控制和单位向量控制各自的优点,控制信号抖振更小,闭环系统稳态性能有了一定改进。