On the solvability of the positive real lemma equations

In this paper, we consider the classical equations of the positive real lemma under the sole assumption that the state matrix A has unmixed spectrum: σ(A)∩σ(−A)=. Without any other system-theoretic assumption (observability, reachability, stability, etc.), we derive a necessary and sufficient condition for the solvability of the positive real lemma equations.     

时变多变量系统辨识的一种方法

本文提出时变多变量系统辨识的一种新方法，并分析了算法的收敛性和稳定性。仿真例子表明所提出算法是有效的。     

“非齐次拟线性双曲型方程组整体经典解”一文的注记

利用常微分方程Cauchy问题的比较引理,证明了一类拟线性双曲型方程Cauchy问题整体经典解的存在性,丰富了"非齐次拟线性双曲型方程组整体经典解"一文的主要结论.     

Nonlinear Consensus Algorithms with Uncertain Couplings

Distributed algorithms for synchronization and consensus in multi‐agent networks are considered. The agents are assumed to be linear of arbitrary order, the interaction topology may switch, and the couplings are uncertain, assumed only to satisfy certain quadratic constraints. Using the Kalman‐Yakubovich‐Popov lemma and absolute stability theory techniques, consensus criteria for the networks of this type are obtained. These criteria extend a number of known results for agents with special dynamics and are close in spirit to the celebrated circle criterion for the stability of Lurie systems.     

基于不完全转移率的连续Markov 跳变奇异系统的H∞ 控制

研究一类不完全转移率信息的Markov跳变奇异系统的H∞控制问题,提出连续Markov跳变奇异系统的新型有界实引理,并将其推广到不完全转移率条件.进一步设计H∞状态反馈控制器,使得闭环系统在转移率部分未知的条件下随机可容许,且满足H∞性能H.所得结论涵盖了奇异矩阵模态依赖情形,且表示为严格线性矩阵不等式形式,利于工程实现.最后,通过仿真算例表明了所提出方法的有效性和优越性.     

A delay‐dependent bounded real lemma for singular LPV systems with time‐variant delay

This paper is concerned with establishing a delay‐dependent bounded real lemma (BRL) for singular linear parameter‐varying (LPV) systems with time‐variant delay. In terms of linear matrix inequality, a delay‐dependent BRL is presented to ensure singular time‐delay LPV systems to be admissible and satisfy a prescribed H_∞ performance level. The BRL is obtained based on the construction of a parameter‐dependent Lyapunov–Krasovskii functional. The effectiveness of the proposed approach is shown by several numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust stabilization of linear discrete-time systems with time-varying input delay

This paper presents a sufficient condition to stabilize linear discrete-time systems with time-varying input delay and model uncertainties. The key idea consists of applying Artstein’s reduction method and the scaled bounded real lemma; the robust stabilization problem is cast as a set of linear matrix inequalities on a transformed delay-free system. Hence, a novel convex characterization of the problem, an alternative to bilinear matrix inequalities in prior literature, is provided. Predictor-based controllers and robust state-feedback stabilization are particular cases of the proposal. Furthermore, numerical examples show that this proposal may improve tolerance against delay variations when compared to other methods available in literature.     

On the Kalman–Yakubovich–Popov lemma for discrete-time positive linear systems: a novel simple proof and some related results

Theorems of alternatives on the feasibility of linear matrix inequalities (LMIs) are used in order to provide novel simple proofs for two considered versions of the Kalman–Yakubovich–Popov (KYP) lemma for discrete-time positive linear systems. Two different and novel recursive methods, to determine whether a positive matrix is or is not Schur, are obtained as an application of an existing connection between the strict inequality version of the KYP lemma for single-input single-output (SISO) discrete-time positive linear systems and a Schur matrix condition. Examples are included which provide illustration on these recursive methods.     

具有执行器容错的汽车主动悬架系统有限频率H∞控制

本文研究了一类具有执行器容错的主动悬架系统有限频率H_∞控制问题.运用广义的Kalman-Yakubovich-Popov(KYP)引理,设计了有限频率H_∞控制器.该控制器不仅能够最大程度地减少路面在4～8 Hz范围内对乘客的影响,还能够保证汽车的悬架行程和车轮的动静载之比在它们允许的范围内.因此所设计的有限频率H_∞控制器不仅能够保证汽车驾驶的舒适性还能够保证汽车驾驶的安全性.为了解决系统状态不完全可测的问题,本文采用了动态输出反馈控制器策略.除此之外,在控制器的设计过程中还考虑了主动悬架系统的参数不确定性以及执行器随机故障的现象.最后,本文基于四分之一汽车主动悬架系统验证了控制器的有效性.