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。     

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.     

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.     

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.     

Hierarchical inversion‐based output tracking control for uncertain autonomous underwater vehicles using extended Kalman filter

In this study, a hierarchical inversion‐based output tracking controller (HIOTC) is developed for an autonomous underwater vehicle (AUV) subject to random uncertainties (e.g., current disturbances, unmodeled dynamics, and parameter variations) and noises (e.g., process and measurement noises). The proposed HIOTC respectively utilizes a combination of feedforward and feedback controls in a hierarchical structure based on the kinematic and dynamic models of the system. Moreover, to obtain uncontaminated or unavailable states for implementing the proposed control law, the extended Kalman filter (EKF) is employed to estimate the system states. Then, the position outputs, orientation, and velocity of the AUV are reached with guaranteed asymptotic stability. The robustness of the proposed HIOTC is verified through injection of random uncertainties into the system model. The closed‐loop stability of the proposed individual subsystems is respectively guaranteed to have uniformly ultimately bounded (UUB) performance based on the Lyapunov stability criteria. In addition, the asymptotic tracking of the overall system is demonstrated using Barbalat's lemma. Finally, the feasibility and effectiveness of the proposed control scheme are evaluated through computer simulations and it is shown that the overall system achieves good asymptotic tracking performance.     

“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.     

A Mechanized Proof of the Basic Perturbation Lemma

We present a complete mechanized proof of the result in homological algebra known as basic perturbation lemma. The proof has been carried out in the proof assistant Isabelle, more concretely, in the implementation of higher-order logic (HOL) available in the system. We report on the difficulties found when dealing with abstract algebra in HOL, and also on the ongoing stages of our project to give a certified version of some of the algorithms present in the Kenzo symbolic computation system. J. Aransay was partially supported by Ministerio de Educación y Ciencia, MTM2006/06513, and by Gobierno de La Rioja ANGI2005/19 and J. Rubio was partially supported by Ministerio de Educación y Ciencia, MTM2006/06513, and by Gobierno de La Rioja ANGI2005/19.