分段线性函数应用于线性时变系统的分析

本文给出了分段线性函数的一些运算性质,利用这一性质对线性时变系统状态方程进行求解,推导出了形式简明、便于应用的递推算法。分段线性函数算法具有较高的分析精度。     

SISO系统参数辨识的局部最优信号

讨论了线性离散时间ＳＩＳＯ系统的参数辨识的最优信号问题，在Ｄ—最优准则下导出了一个离线辨识的局部最优信号算法，并且根据该算法为某水轮机组系统参数辨识，设计出一局部最优试验信号．     

变系数线性系统渐近稳定性的一种判定方法

讨论了ｎ维变系数线性系统的渐近稳定性的判定方法，通过求该系统的Ｈｅｒｍｉｔ矩阵的广义特征根给出了变系数线性系统的渐近稳定性的几个判定定理。     

脉冲响应的一种快速算法及其应用

本文提出一种脉冲响应解析解的求取方法。该方法通过有限次代数运算，可以得到系统脉冲响应的精确解，且易于程序实现。该方法可应用到时域矩阵方法中的时域矩阵求取，与文献［３］中方法相比，本文方法求取时域矩阵运算量小，计算结果为解析解，且能适用于刚性方程求解。     

Higher‐order modal transformation for reduced‐order modeling of linear systems undergoing global parametric variations

Previously, a novel parametric reduced‐order model technique for linear systems was developed based on a frequency‐domain formulation and the so‐called modally equivalent perturbed system. The main advantage of the scheme is that it isolates all the perturbed matrices into a forcing term, allowing for a simple and powerful analysis based on the ordinary differential equation with the forcing input. It was shown that when the parameter variation is limited to a finite dimension, it yields exceptionally accurate reduced‐order models for a wide range of parameter values. In this paper, the original method is improved to cover a larger‐dimensional domain and the global domain of the variation by adding higher‐order terms in the formulation. It is shown that when expressed in powers of incremental matrices, the new formula resembles a well‐known series expansion. The improved parametric reduced‐order model is demonstrated for a computational fluid dynamics model of unsteady air flow around a two‐dimensional airfoil in subsonic flows with Mach variation.     

Explicit Solution for a Class of Discrete‐Time Algebraic Riccati Equations

In the present paper we obtain an explicit closed‐form solution for the discrete‐time algebraic Riccati equation (DTARE) with vanishing state weight, whenever the unstable eigenvalues are distinct. We discuss links to current algorithmic solutions and observe that the AREs in such a class solve on one hand the infimal signal‐to‐noise ratio (SNR) problem, whilst on the other hand, in their dual form they solve a Kalman filter problem. We then extend the main result to an example case of the optimal linear quadratic regulator gain. We relax some of the assumptions behind the main result and conclude with possible future directions for the present work.     

广义Vandermonde方程组的有效快速算法

基于求解Vandermonde方程组的Bjorck-Pereyra算法,本文给出了求解广义Vandermonde方程组的有效快速算法,所需的计算量为O(n2)。数值算例表明,与求解Vandermonde方程组的Gohberg-Kailath-Koltracht算法和Gauss消元法相比,本文的算法具有更高的计算精度。     

Efficient Solution of A, x ( k )?= b ( k ) Using A ?1

In this work, we consider the problem of solving , , where b ^(k+1) = f(x ^(k)). We show that when A is a full matrix and , where depends on the specific software and hardware setup, it is faster to solve for by explicitly evaluating the inverse matrix A ⁻¹ rather than through the LU decomposition of A. We also show that the forward error is comparable in both methods, regardless of the condition number of A.     

Approximate causal output tracking for linear perturbed systems via sliding mode control

ABSTRACT

A new approach to the solution of what is termed causal output tracking problem for linear time-invariant systems in the presence of both matched and unmatched unmodelled disturbances is presented. The proposed solution is addressed through the design of a dynamic steady state estimator based on the desired system structure and an observer, considering the reference as the system output. The unmatched disturbance is estimated and used in the steady state estimator to achieve invariance, while the matched disturbance robustness is provided via sliding mode control using the super-twisting algorithm. A useful application of the presented techniques is output tracking for non-minimum phase systems; thus, the performed simulation results confirm the effectiveness of the proposed control scheme for this kind of systems.     

Improved Input and State Estimation for Linear Stochastic Systems with Direct Feedthrough

This paper is concerned with the problem of joint input and state estimation for linear stochastic systems with direct feedthrough. Based on the fact that each unknown input between any two time steps is always bounded, a novel improved algorithm is proposed. Compared with existing results, this algorithm can effectively enhance estimation accuracy. Moreover, the stability of the algorithm is also discussed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.