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.     

Linear Operator Inequalities for Strongly Stable Weakly Regular Linear Systems

We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov function and to singular optimal control problems with a nonnegative definite quadratic cost functional. We split our problem into two subproblems: the existence of spectral factors of the nonnegative Popov function and the existence of a certain extended output map. Sufficient conditions for the solvability of the first problem are known and for the case that A has compact resolvent and its eigenvectors form a Riesz basis for the state space, we give an explicit solution to the second problem in terms of A, B, C and the spectral factor. The applicability of these results is demonstrated by various heat equation examples satisfying a positive-real condition. If (A, B) is approximately controllable, we obtain an alternative criterion for the existence of an extended output operator which is applicable to retarded systems. The above results have been used to design adaptive observers for positive-real infinite-dimensional systems. Date received: July 25, 1997. Date revised: February 10, 2001.     

Minimal representations of continuous-time processes having spectral density with zeros in the extended imaginary axis

Given a process y with stationary increments and rational incremental spectral density Φ(s), we parametrize minimal state-space representations of dy. We consider the case when Φ(s) may have zeros on the imaginary axis including infinity and we analyze the zero structure of each state-space representation.     

Existence of unmixed solutions of the discrete-time algebraic Riccati equation and a nonstrictly bounded real lemma

The existence of a solution of the discrete-time algebraic Riccati equation is established assuming modulus controllability and positive semidefiniteness on the unit circle of the Popov function. As an application a nonstrictly bounded real lemma is obtained.     

An H∞ deconvolution filter and its application to ultrasonic nondestructive evaluation of materials

Deconvolution can be a valuable technique for interpreting results of ultrasonic nondestructive evaluation (NDE) tests of materials. This is especially true for state of the art hybrid materials. In this paper, a new H_∞ deconvolution filter is presented. The filter is applied to typical ultrasonic NDE data, including through-transmission data for aluminum and composite samples. The results are compared to those obtained from a Wiener deconvolution filter. The performance of the H_∞ filter is as good or better than the performance of the Wiener filter.     

A generalized Ufnarovski graph

An important tool for studying standard finitely presented algebras is the Ufnarovski graph. In this paper we extend the use of the Ufnarovski graph to automaton algebras, introducing the generalized Ufnarovski graph. As an application, we show how this construction can be used to test Noetherianity of automaton algebras.     

Well-known bound for the VC-dimension made easy

The Sauer lemma gives an upper bound for the cardinality of a set with given Vapnik-Chervonenkis dimension (VC-dimension). This paper presents a simple algebraic proof.     

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.     

混沌细胞神经网络的自适应同步及其在保密通信中的应用

针对具有时变时滞和扰动的混沌细胞神经网络的同步问题,提出一种自适应同步方法。利用Lyapunov稳定性理论、Barbalat引理和自适应控制方法,给出易于实现的自适应同步控制律,实现了误差系统的全局渐近稳定。所得自适应同步控制律具有一定的鲁棒性。最后利用混沌掩盖技术将研究结果应用到保密通信中。数值仿真结果表明,该方法所设计的自适应控制律具有良好的控制效果。