ℋ︁∞ and l2–l∞ filtering for two‐dimensional linear parameter‐varying systems

In this paper, the ??_∞ and l₂–l_∞ filtering problem is investigated for two‐dimensional (2‐D) discrete‐time linear parameter‐varying (LPV) systems. Based on the well‐known Fornasini–Marchesini local state‐space (FMLSS) model, the mathematical model of 2‐D systems under consideration is established by incorporating the parameter‐varying phenomenon. The purpose of the problem addressed is to design full‐order ??_∞ and l₂–l_∞ filters such that the filtering error dynamics is asymptotic stable and the prescribed noise attenuation levels in ??_∞ and l₂–l_∞ senses can be achieved, respectively. Sufficient conditions are derived for existence of such filters in terms of parameterized linear matrix inequalities (PLMIs), and the corresponding filter synthesis problem is then transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is exploited to demonstrate the usefulness and effectiveness of the proposed design method. Copyright © 2007 John Wiley & Sons, Ltd.     

Theory of Fuzzy Generalized Morphisms and Relational Inequalities

We present here the theory of generalized morphisms and fuzzy relational inequalities and discuss some of these applications. Results presented in this paper extend the work of Bandler and Kohout (1986) ["On the general theory of relational morphisms", International Journal of General Systems, 13, pp. 47-66] published in this journal previously, to relational systems based on residuated t-norm fuzzy logics.     

分数阶系统线性矩阵不等式稳定判据的改进与鲁棒镇定: 0<α<1的情况

针对确定的分数阶系统,通过发掘其稳定区域与线性矩阵不等式(LMI)之间的联系,提出改进的LMI稳定判据.与已有结果相比,该判据形式简洁,求解变量少,且不含复矩阵变量,能够直接应用于控制器设计而不带来任何保守性,克服了原判据存在的主要缺点.然后基于该判据,进一步研究了当分数阶系统具有多胞型不确定时的鲁棒镇定控制器的设计方法.最后,仿真结果表明该方法的有效性.     

Computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations

This paper is concerned with the computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations. Firstly, a delay-independent condition on the robust stability is presented and a method to determine the maximum upper bound of robust stability is given. Then, a delay-dependent robust stability condition is provided. All results are given in terms of linear matrix inequalities where efficient solution procedures are available. Numerical examples have shown that the results are less conservative than some previous established bounds.     

H ∞ control of networked control systems with state quantisation

This article addresses the problem of controller design for networked control systems over digital communication. The systems under consideration are stabilised via state feedback, where the effects of sampled signal, state quantisation, network-induced delay and packet dropout are considered. The proposed delay-dependent stability criteria are formulated in the form of a linear matrix inequality, which ensure asymptotic stability and a prescribed H _∞ performance level for networked control systems with admissible uncertainties. Maximum allowable delay bound of networked control systems is obtained by solving a convex optimisation problem. Furthermore, a numerical example is given to illustrate the effectiveness of the main result.     

State feedback control of interval type-2 Takagi–Sugeno fuzzy systems via interval type-2 regional switching fuzzy controllers

The interval type-2 Takagi–Sugeno fuzzy systems have been proposed to handle nonlinear systems subject to parameter uncertainties. In this paper, a new type of state feedback controller, namely, interval type-2 regional switching fuzzy controller, is proposed to conceive less-conservative stabilisation conditions, which is switched by basing on the values of system states. To further reduce the conservativeness in the stability analysis, the information of lower and upper membership functions is also considered. Stability conditions for the interval type-2 fuzzy closed-loop systems are presented in the form of linear matrix inequalities (LMIs). Simulation examples are provided to illustrate the effectiveness of the proposed method.     

Robust control oriented identification of errors-in-variables models based on normalised coprime factors

A robust control oriented identification approach is proposed to deal with the identification of errors-in-variables models (EIVMs), which are corrupted with input and output noises. Based on normalised coprime factor model (NCFM) representations, a frequency-domain perturbed NCFM for an EIVM is derived according to a geometrical explanation for the v-gap metric. As a result, identification of the EIVM is converted into that of the NCFM. Besides an identified nominal NCFM, its worst case error has to be quantified. Unlike other traditional control-oriented identification methods, the v-gap metric is employed to measure the uncertainties including a priori information on the disturbing noises and the worst case error for the resulting nominal NCFM. Since this metric is also used as an optimisation criterion, the associate parameter estimation problem can be effectively solved by linear matrix inequalities. Finally, a numerical simulation shows the effectiveness of the proposed method.