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Dan Peng,Jing Zhang,Chang-chun Hua,Chang Gao 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.2
Two recent Lyapunov-based methods: delay-partitioning approach and Jensen inequality approach, have reduced the conservatism and the complexity of the stability result for one-dimensional (1-D) time-delay systems, respectively. This paper concerns the analysis of delay-dependent stability for two-dimensional (2-D) discrete systems with interval time-varying delays. By applying a delay partitioning-based Lyapunov function combining with the approaches of 2-D Jensen inequalities, a new delay-dependent stability criterion is derived in terms of linear matrix inequality (LMI). In addition to delay dependence, the obtained criterion is also dependent on the partition size. It is rigorously proved that the authors’ result reduces the conservativeness and computational burden than some recent ones. Numerical examples show the effectiveness and advantage of our result.
Pin-Lin Liu 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.8
This paper is concerned with the problem of delay-derivative-dependent stability analysis for Markovian jumping neutral-type interval time-varying delay systems with mixed delays. The first, based on the LyapunovKrasovskii stability theory for functional differential equations and the linear matrix inequality approach, a delayrange-dependent condition for neutral-type Markovian jumping systems (NMJSs) with time-varying delays is obtained, which can guarantee global asymptotical stability of these NMJSs. Unlike the previous methods, the upper bound of the discrete delay and neutral delay derivative is taken into consideration even if this upper bound is larger than or equal to 1 (h˙(t) < 1, τ˙(t) < 1). It is proved that the obtained results are less conservative than the existing ones. In our result, the time-varying delays are only assumed to be bounded. This has undoubtedly extended its application range. To better handle the problem on stability for neutral control systems, in which time-varying delaywas involved, a stability criterion with less conservatism was put forward. Moreover, because our results in thispaper are all based on the linear matrix inequality (LMI) approach, we can utilize Matlab’s LMI Control Toolboxto verify the global stability of correlation systems conveniently. As far as we are aware, this paper seems to be thefirst to discuss stability problems for neutral-type Markovian jumping systems with delay-derivative-dependenceand delay-range-dependence.
Xinghua Zhang,Yantao Wang,Xiaofei Fan 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.2
In this paper, the stability analysis problem of linear systems with an interval time-varying delay is investigated. Firstly, an augmented Lyapunov-Krasovskii functional is constructed, which includes more informationof the delay’s range and the delay’s derivative. Secondly, based on two improved integral inequalities which are lessconservative than Jensen’s integral inequalities, a delay-range-partition (DRP) approach is proposed to estimate theupper bound of the derivative of the augmented Lyapunov-Krasovskii functional. Then, less conservative stabilitycriteria in the form of linear matrix inequality (LMI) are established no matter whether the lower bound of delayis zero or not. Finally, to illustrate the effectiveness of the stability criteria proposed in this paper, two numericalexamples are given, and their results are compared with the existing results.
Haiyang Zhang,Lianglin Xiong,Qing Miao,Yanmeng Wang 제어로봇시스템학회 2015 제어로봇시스템학회 국제학술대회 논문집 Vol.2015 No.10
This article addressed the problem of delay-dependent stability criteria for linear time system with interval time-delay. Firstly, we proposed a new inequality based on the Fourier Theory, more precisely on theWirtingers inequalities, which is proved to encompass the Jensens inequality. Secondly, a less conservative stability condition is established in terms of linear matrix inequalities by employing delay-partition idea and Lyapunov functional method. Finally, in order to illustrate the potential gain of employing this new inequality with respect to the Jensens one and the effectiveness of the proposed results,an application to time-delay analysis is provided.
상태와 입력에 구간 시변 시간지연을 가지는 불확실 이산시간 특이시스템의 지연 종속 강인 H<SUB>∞</SUB> 제어
金鍾海(Jong-Hae Kim) 대한전기학회 2009 전기학회논문지 Vol.58 No.1
In this paper, we consider the design problem of delay-dependent robust H∞ controller of discrete-time descriptor systems with parameter uncertainties and interval time-varying delays in state and control input by delay-dependent LMI (linear matrix inequality) technique. A new delay-dependent bounded real lemma for discrete-time descriptor systems with time-varying delays is derived. The condition for the existence of robust H∞ controller and the robust H∞ state feedback control law are proposed by LMI approach. A numerical example is demonstrated to show the validity of the design method.
Mixed-delay-dependent L2-L∞ Filtering for Neutral Stochastic Systems with Time-varying Delays
Yaobo Yu,Xiaoling Tang,Tao Li,Shumin Fei 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.11
This paper studies the issue on mixed-delay-dependent L2-L∞ filter design for a class of neutral stochastic system with time-varying delays. By making full use of the information and interrelationship of time-delays, an augmented Lyapunov-Krasovskii functional (LKF) is constructed for the filtering error system. In the derivation process, some Writinger-based integral inequalities and an extend reciprocal convex technique (ERCT) are utilized to estimate the lower bound of L2-L∞ disturbance attention level. Based on the derived stability criteria, two sufficient conditions on the existence of full-order L2-L∞ filter are presented in terms of linear matrix inequalities(LMIs), which can be easily tested and less conservative. Finally, two cases in an example are given to demonstrate the effectiveness of the proposed approach.
시변 시간지연을 가지는 불확실 특이시스템의 지연 종속 강인 H<SUB>∞</SUB> 필터링
김종해(Jong-Hae Kim) 대한전기학회 2009 전기학회논문지 Vol.58 No.9
This paper is concerned with the problem of delay-dependent robust H∞ filtering for uncertain descriptor systems with time-varying delay. The considering uncertainty is convex compact set of polytoic type. The purpose is the design of a linear filter such that the resulting filtering error descriptor system is regular, impulse-free, and asymptotically stable with H∞ norm bound. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) for delayed descriptor systems is derived. Based on the derived BRL, a robust H∞ filter is designed in terms of linear matrix inequaltity (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method.